Created an UncertainDouble class for uncertainty operations.

7 files changed, 885 insertions, 400 deletions

diff --git a/.settings/org.eclipse.jdt.core.prefs b/.settings/org.eclipse.jdt.core.prefs
index ea7a397..f77f6a1 100644
--- a/.settings/org.eclipse.jdt.core.prefs
+++ b/.settings/org.eclipse.jdt.core.prefs
@@ -1,4 +1,13 @@
 eclipse.preferences.version=1
+org.eclipse.jdt.core.compiler.annotation.inheritNullAnnotations=disabled
+org.eclipse.jdt.core.compiler.annotation.missingNonNullByDefaultAnnotation=ignore
+org.eclipse.jdt.core.compiler.annotation.nonnull=org.eclipse.jdt.annotation.NonNull
+org.eclipse.jdt.core.compiler.annotation.nonnull.secondary=
+org.eclipse.jdt.core.compiler.annotation.nonnullbydefault=org.eclipse.jdt.annotation.NonNullByDefault
+org.eclipse.jdt.core.compiler.annotation.nonnullbydefault.secondary=
+org.eclipse.jdt.core.compiler.annotation.nullable=org.eclipse.jdt.annotation.Nullable
+org.eclipse.jdt.core.compiler.annotation.nullable.secondary=
+org.eclipse.jdt.core.compiler.annotation.nullanalysis=disabled
 org.eclipse.jdt.core.compiler.codegen.inlineJsrBytecode=enabled
 org.eclipse.jdt.core.compiler.codegen.targetPlatform=1.8
 org.eclipse.jdt.core.compiler.codegen.unusedLocal=preserve
@@ -6,11 +15,102 @@ org.eclipse.jdt.core.compiler.compliance=1.8
 org.eclipse.jdt.core.compiler.debug.lineNumber=generate
 org.eclipse.jdt.core.compiler.debug.localVariable=generate
 org.eclipse.jdt.core.compiler.debug.sourceFile=generate
+org.eclipse.jdt.core.compiler.problem.APILeak=warning
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+org.eclipse.jdt.core.compiler.problem.autoboxing=ignore
+org.eclipse.jdt.core.compiler.problem.comparingIdentical=warning
+org.eclipse.jdt.core.compiler.problem.deadCode=warning
+org.eclipse.jdt.core.compiler.problem.deprecation=warning
+org.eclipse.jdt.core.compiler.problem.deprecationInDeprecatedCode=disabled
+org.eclipse.jdt.core.compiler.problem.deprecationWhenOverridingDeprecatedMethod=enabled
+org.eclipse.jdt.core.compiler.problem.discouragedReference=warning
+org.eclipse.jdt.core.compiler.problem.emptyStatement=ignore
 org.eclipse.jdt.core.compiler.problem.enablePreviewFeatures=disabled
 org.eclipse.jdt.core.compiler.problem.enumIdentifier=error
+org.eclipse.jdt.core.compiler.problem.explicitlyClosedAutoCloseable=warning
+org.eclipse.jdt.core.compiler.problem.fallthroughCase=error
+org.eclipse.jdt.core.compiler.problem.fatalOptionalError=enabled
+org.eclipse.jdt.core.compiler.problem.fieldHiding=ignore
+org.eclipse.jdt.core.compiler.problem.finalParameterBound=warning
+org.eclipse.jdt.core.compiler.problem.finallyBlockNotCompletingNormally=warning
 org.eclipse.jdt.core.compiler.problem.forbiddenReference=warning
+org.eclipse.jdt.core.compiler.problem.hiddenCatchBlock=warning
+org.eclipse.jdt.core.compiler.problem.includeNullInfoFromAsserts=disabled
+org.eclipse.jdt.core.compiler.problem.incompatibleNonInheritedInterfaceMethod=warning
+org.eclipse.jdt.core.compiler.problem.incompleteEnumSwitch=warning
+org.eclipse.jdt.core.compiler.problem.indirectStaticAccess=ignore
+org.eclipse.jdt.core.compiler.problem.localVariableHiding=ignore
+org.eclipse.jdt.core.compiler.problem.methodWithConstructorName=warning
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+org.eclipse.jdt.core.compiler.problem.missingHashCodeMethod=error
+org.eclipse.jdt.core.compiler.problem.missingOverrideAnnotation=warning
+org.eclipse.jdt.core.compiler.problem.missingOverrideAnnotationForInterfaceMethodImplementation=enabled
+org.eclipse.jdt.core.compiler.problem.missingSerialVersion=warning
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+org.eclipse.jdt.core.compiler.problem.noImplicitStringConversion=warning
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+org.eclipse.jdt.core.compiler.problem.nonnullTypeVariableFromLegacyInvocation=warning
+org.eclipse.jdt.core.compiler.problem.nullAnnotationInferenceConflict=error
+org.eclipse.jdt.core.compiler.problem.nullReference=error
+org.eclipse.jdt.core.compiler.problem.nullSpecViolation=error
+org.eclipse.jdt.core.compiler.problem.nullUncheckedConversion=warning
+org.eclipse.jdt.core.compiler.problem.overridingPackageDefaultMethod=warning
+org.eclipse.jdt.core.compiler.problem.parameterAssignment=info
+org.eclipse.jdt.core.compiler.problem.pessimisticNullAnalysisForFreeTypeVariables=warning
+org.eclipse.jdt.core.compiler.problem.possibleAccidentalBooleanAssignment=warning
+org.eclipse.jdt.core.compiler.problem.potentialNullReference=warning
+org.eclipse.jdt.core.compiler.problem.potentiallyUnclosedCloseable=info
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+org.eclipse.jdt.core.compiler.problem.redundantNullAnnotation=warning
+org.eclipse.jdt.core.compiler.problem.redundantNullCheck=info
+org.eclipse.jdt.core.compiler.problem.redundantSpecificationOfTypeArguments=info
+org.eclipse.jdt.core.compiler.problem.redundantSuperinterface=info
+org.eclipse.jdt.core.compiler.problem.reportMethodCanBePotentiallyStatic=ignore
+org.eclipse.jdt.core.compiler.problem.reportMethodCanBeStatic=info
 org.eclipse.jdt.core.compiler.problem.reportPreviewFeatures=ignore
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+org.eclipse.jdt.core.compiler.problem.staticAccessReceiver=info
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+org.eclipse.jdt.core.compiler.problem.suppressWarningsNotFullyAnalysed=ignore
+org.eclipse.jdt.core.compiler.problem.syntacticNullAnalysisForFields=disabled
+org.eclipse.jdt.core.compiler.problem.syntheticAccessEmulation=ignore
+org.eclipse.jdt.core.compiler.problem.terminalDeprecation=error
+org.eclipse.jdt.core.compiler.problem.typeParameterHiding=warning
+org.eclipse.jdt.core.compiler.problem.unavoidableGenericTypeProblems=disabled
+org.eclipse.jdt.core.compiler.problem.uncheckedTypeOperation=warning
+org.eclipse.jdt.core.compiler.problem.unclosedCloseable=warning
+org.eclipse.jdt.core.compiler.problem.undocumentedEmptyBlock=ignore
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 org.eclipse.jdt.core.compiler.processAnnotations=disabled
 org.eclipse.jdt.core.compiler.release=disabled
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diff --git a/src/org/unitConverter/math/DecimalComparison.java b/src/org/unitConverter/math/DecimalComparison.java
index 859e8da..0f5b91e 100644
--- a/src/org/unitConverter/math/DecimalComparison.java
+++ b/src/org/unitConverter/math/DecimalComparison.java
@@ -27,42 +27,45 @@ import java.math.BigDecimal;
  */
 public final class DecimalComparison {
 	/**
-	 * The value used for double comparison. If two double values are within this value multiplied by the larger value,
-	 * they are considered equal.
+	 * The value used for double comparison. If two double values are within this
+	 * value multiplied by the larger value, they are considered equal.
 	 * 
 	 * @since 2019-03-18
 	 * @since v0.2.0
 	 */
 	public static final double DOUBLE_EPSILON = 1.0e-15;
-
+	
 	/**
-	 * The value used for float comparison. If two float values are within this value multiplied by the larger value,
-	 * they are considered equal.
+	 * The value used for float comparison. If two float values are within this
+	 * value multiplied by the larger value, they are considered equal.
 	 * 
 	 * @since 2019-03-18
 	 * @since v0.2.0
 	 */
 	public static final float FLOAT_EPSILON = 1.0e-6f;
-
+	
 	/**
 	 * Tests for equality of double values using {@link #DOUBLE_EPSILON}.
 	 * <p>
-	 * <strong>WARNING: </strong>this method is not technically transitive. If a and b are off by slightly less than
-	 * {@code epsilon * max(abs(a), abs(b))}, and b and c are off by slightly less than
-	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c) will both return true, but equals(a, c)
-	 * will return false. However, this situation is very unlikely to ever happen in a real programming situation.
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
 	 * <p>
 	 * If this does become a concern, some ways to solve this problem:
 	 * <ol>
-	 * <li>Raise the value of epsilon using {@link #equals(double, double, double)} (this does not make a violation of
-	 * transitivity impossible, it just significantly reduces the chances of it happening)
-	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a violation of transitivity 100% impossible)
+	 * <li>Raise the value of epsilon using
+	 * {@link #equals(double, double, double)} (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
 	 * </ol>
 	 * 
-	 * @param a
-	 *            first value to test
-	 * @param b
-	 *            second value to test
+	 * @param a first value to test
+	 * @param b second value to test
 	 * @return whether they are equal
 	 * @since 2019-03-18
 	 * @since v0.2.0
@@ -71,57 +74,61 @@ public final class DecimalComparison {
 	public static final boolean equals(final double a, final double b) {
 		return DecimalComparison.equals(a, b, DOUBLE_EPSILON);
 	}
-
+	
 	/**
 	 * Tests for double equality using a custom epsilon value.
 	 * 
 	 * <p>
-	 * <strong>WARNING: </strong>this method is not technically transitive. If a and b are off by slightly less than
-	 * {@code epsilon * max(abs(a), abs(b))}, and b and c are off by slightly less than
-	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c) will both return true, but equals(a, c)
-	 * will return false. However, this situation is very unlikely to ever happen in a real programming situation.
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
 	 * <p>
 	 * If this does become a concern, some ways to solve this problem:
 	 * <ol>
-	 * <li>Raise the value of epsilon (this does not make a violation of transitivity impossible, it just significantly
-	 * reduces the chances of it happening)
-	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a violation of transitivity 100% impossible)
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
 	 * </ol>
 	 * 
-	 * @param a
-	 *            first value to test
-	 * @param b
-	 *            second value to test
-	 * @param epsilon
-	 *            allowed difference
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
 	 * @return whether they are equal
 	 * @since 2019-03-18
 	 * @since v0.2.0
 	 */
-	public static final boolean equals(final double a, final double b, final double epsilon) {
+	public static final boolean equals(final double a, final double b,
+			final double epsilon) {
 		return Math.abs(a - b) <= epsilon * Math.max(Math.abs(a), Math.abs(b));
 	}
-
+	
 	/**
 	 * Tests for equality of float values using {@link #FLOAT_EPSILON}.
 	 * 
 	 * <p>
-	 * <strong>WARNING: </strong>this method is not technically transitive. If a and b are off by slightly less than
-	 * {@code epsilon * max(abs(a), abs(b))}, and b and c are off by slightly less than
-	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c) will both return true, but equals(a, c)
-	 * will return false. However, this situation is very unlikely to ever happen in a real programming situation.
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
 	 * <p>
 	 * If this does become a concern, some ways to solve this problem:
 	 * <ol>
-	 * <li>Raise the value of epsilon using {@link #equals(float, float, float)} (this does not make a violation of
-	 * transitivity impossible, it just significantly reduces the chances of it happening)
-	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a violation of transitivity 100% impossible)
+	 * <li>Raise the value of epsilon using {@link #equals(float, float, float)}
+	 * (this does not make a violation of transitivity impossible, it just
+	 * significantly reduces the chances of it happening)
+	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a
+	 * violation of transitivity 100% impossible)
 	 * </ol>
 	 * 
-	 * @param a
-	 *            first value to test
-	 * @param b
-	 *            second value to test
+	 * @param a first value to test
+	 * @param b second value to test
 	 * @return whether they are equal
 	 * @since 2019-03-18
 	 * @since v0.2.0
@@ -129,53 +136,121 @@ public final class DecimalComparison {
 	public static final boolean equals(final float a, final float b) {
 		return DecimalComparison.equals(a, b, FLOAT_EPSILON);
 	}
-
+	
 	/**
 	 * Tests for float equality using a custom epsilon value.
 	 * 
 	 * <p>
-	 * <strong>WARNING: </strong>this method is not technically transitive. If a and b are off by slightly less than
-	 * {@code epsilon * max(abs(a), abs(b))}, and b and c are off by slightly less than
-	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c) will both return true, but equals(a, c)
-	 * will return false. However, this situation is very unlikely to ever happen in a real programming situation.
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
 	 * <p>
 	 * If this does become a concern, some ways to solve this problem:
 	 * <ol>
-	 * <li>Raise the value of epsilon (this does not make a violation of transitivity impossible, it just significantly
-	 * reduces the chances of it happening)
-	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a violation of transitivity 100% impossible)
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code float} (this will make a
+	 * violation of transitivity 100% impossible)
 	 * </ol>
 	 * 
-	 * @param a
-	 *            first value to test
-	 * @param b
-	 *            second value to test
-	 * @param epsilon
-	 *            allowed difference
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
 	 * @return whether they are equal
 	 * @since 2019-03-18
 	 * @since v0.2.0
 	 */
-	public static final boolean equals(final float a, final float b, final float epsilon) {
+	public static final boolean equals(final float a, final float b,
+			final float epsilon) {
 		return Math.abs(a - b) <= epsilon * Math.max(Math.abs(a), Math.abs(b));
 	}
-
+	
+	/**
+	 * Tests for equality of {@code UncertainDouble} values using
+	 * {@link #DOUBLE_EPSILON}.
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon using
+	 * {@link #equals(UncertainDouble, UncertainDouble, double)} (this does not
+	 * make a violation of transitivity impossible, it just significantly reduces
+	 * the chances of it happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a first value to test
+	 * @param b second value to test
+	 * @return whether they are equal
+	 * @since 2020-09-07
+	 * @see #hashCode(double)
+	 */
+	public static final boolean equals(final UncertainDouble a,
+			final UncertainDouble b) {
+		return DecimalComparison.equals(a.value(), b.value())
+				&& DecimalComparison.equals(a.uncertainty(), b.uncertainty());
+	}
+	
+	/**
+	 * Tests for {@code UncertainDouble} equality using a custom epsilon value.
+	 * 
+	 * <p>
+	 * <strong>WARNING: </strong>this method is not technically transitive. If a
+	 * and b are off by slightly less than {@code epsilon * max(abs(a), abs(b))},
+	 * and b and c are off by slightly less than
+	 * {@code epsilon * max(abs(b), abs(c))}, then equals(a, b) and equals(b, c)
+	 * will both return true, but equals(a, c) will return false. However, this
+	 * situation is very unlikely to ever happen in a real programming situation.
+	 * <p>
+	 * If this does become a concern, some ways to solve this problem:
+	 * <ol>
+	 * <li>Raise the value of epsilon (this does not make a violation of
+	 * transitivity impossible, it just significantly reduces the chances of it
+	 * happening)
+	 * <li>Use {@link BigDecimal} instead of {@code double} (this will make a
+	 * violation of transitivity 100% impossible)
+	 * </ol>
+	 * 
+	 * @param a       first value to test
+	 * @param b       second value to test
+	 * @param epsilon allowed difference
+	 * @return whether they are equal
+	 * @since 2019-03-18
+	 * @since v0.2.0
+	 */
+	public static final boolean equals(final UncertainDouble a,
+			final UncertainDouble b, final double epsilon) {
+		return DecimalComparison.equals(a.value(), b.value(), epsilon)
+				&& DecimalComparison.equals(a.uncertainty(), b.uncertainty(),
+						epsilon);
+	}
+	
 	/**
-	 * Takes the hash code of doubles. Values that are equal according to {@link #equals(double, double)} will have the
-	 * same hash code.
+	 * Takes the hash code of doubles. Values that are equal according to
+	 * {@link #equals(double, double)} will have the same hash code.
 	 * 
-	 * @param d
-	 *            double to hash
+	 * @param d double to hash
 	 * @return hash code of double
 	 * @since 2019-10-16
 	 */
 	public static final int hash(final double d) {
 		return Float.hashCode((float) d);
 	}
-
+	
 	// You may NOT get any DecimalComparison instances
 	private DecimalComparison() {
 		throw new AssertionError();
 	}
-
+	
 }
diff --git a/src/org/unitConverter/math/UncertainDouble.java b/src/org/unitConverter/math/UncertainDouble.java
new file mode 100644
index 0000000..e948df9
--- /dev/null
+++ b/src/org/unitConverter/math/UncertainDouble.java
@@ -0,0 +1,411 @@
+/**
+ * @since 2020-09-07
+ */
+package org.unitConverter.math;
+
+import java.math.BigDecimal;
+import java.math.RoundingMode;
+import java.util.Objects;
+import java.util.regex.Matcher;
+import java.util.regex.Pattern;
+
+/**
+ * A double with an associated uncertainty value. For example, 3.2 ± 0.2.
+ * <p>
+ * All methods in this class throw a NullPointerException if any of their
+ * arguments is null.
+ *
+ * @since 2020-09-07
+ */
+public final class UncertainDouble implements Comparable<UncertainDouble> {
+	/**
+	 * The exact value 0
+	 */
+	public static final UncertainDouble ZERO = UncertainDouble.of(0, 0);
+	
+	/**
+	 * A regular expression that can recognize toString forms
+	 */
+	private static final Pattern TO_STRING = Pattern
+			.compile("([a-zA-Z_0-9\\.\\,]+)" // a number
+					// optional "± [number]"
+					+ "(?:\\s*(?:±|\\+-)\\s*([a-zA-Z_0-9\\.\\,]+))?");
+	
+	/**
+	 * Parses a string in the form of {@link UncertainDouble#toString(boolean)}
+	 * and returns the corresponding {@code UncertainDouble} instance.
+	 * <p>
+	 * This method allows some alternative forms of the string representation,
+	 * such as using "+-" instead of "±".
+	 * 
+	 * @param s string to parse
+	 * @return {@code UncertainDouble} instance
+	 * @throws IllegalArgumentException if the string is invalid
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble fromString(String s) {
+		Objects.requireNonNull(s, "s may not be null");
+		final Matcher matcher = TO_STRING.matcher(s);
+		
+		double value, uncertainty;
+		try {
+			value = Double.parseDouble(matcher.group(1));
+		} catch (IllegalStateException | NumberFormatException e) {
+			throw new IllegalArgumentException(
+					"String " + s + " not in correct format.");
+		}
+		
+		final String uncertaintyString = matcher.group(2);
+		if (uncertaintyString == null) {
+			uncertainty = 0;
+		} else {
+			try {
+				uncertainty = Double.parseDouble(uncertaintyString);
+			} catch (final NumberFormatException e) {
+				throw new IllegalArgumentException(
+						"String " + s + " not in correct format.");
+			}
+		}
+		
+		return UncertainDouble.of(value, uncertainty);
+	}
+	
+	/**
+	 * Gets an {@code UncertainDouble} from its value and <b>absolute</b>
+	 * uncertainty.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble of(double value, double uncertainty) {
+		return new UncertainDouble(value, uncertainty);
+	}
+	
+	/**
+	 * Gets an {@code UncertainDouble} from its value and <b>relative</b>
+	 * uncertainty.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public static final UncertainDouble ofRelative(double value,
+			double relativeUncertainty) {
+		return new UncertainDouble(value, value * relativeUncertainty);
+	}
+	
+	private final double value;
+	
+	private final double uncertainty;
+	
+	/**
+	 * @param value
+	 * @param uncertainty
+	 * @since 2020-09-07
+	 */
+	private UncertainDouble(double value, double uncertainty) {
+		this.value = value;
+		// uncertainty should only ever be positive
+		this.uncertainty = Math.abs(uncertainty);
+	}
+	
+	/**
+	 * Compares this {@code UncertainDouble} with another
+	 * {@code UncertainDouble}.
+	 * <p>
+	 * This method only compares the values, not the uncertainties. So 3.1 ± 0.5
+	 * is considered less than 3.2 ± 0.5, even though they are equivalent.
+	 * <p>
+	 * <b>Note:</b> The natural ordering of this class is inconsistent with
+	 * equals. Specifically, if two {@code UncertainDouble} instances {@code a}
+	 * and {@code b} have the same value but different uncertainties,
+	 * {@code a.compareTo(b)} will return 0 but {@code a.equals(b)} will return
+	 * {@code false}.
+	 */
+	@Override
+	public final int compareTo(UncertainDouble o) {
+		return Double.compare(this.value, o.value);
+	}
+	
+	/**
+	 * Returns the quotient of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble dividedBy(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.ofRelative(this.value / other.value, Math
+				.hypot(this.relativeUncertainty(), other.relativeUncertainty()));
+	}
+	
+	/**
+	 * Returns the quotient of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble dividedByExact(double other) {
+		return UncertainDouble.of(this.value / other, this.uncertainty / other);
+	}
+	
+	@Override
+	public final boolean equals(Object obj) {
+		if (this == obj)
+			return true;
+		if (!(obj instanceof UncertainDouble))
+			return false;
+		final UncertainDouble other = (UncertainDouble) obj;
+		if (Double.doubleToLongBits(this.uncertainty) != Double
+				.doubleToLongBits(other.uncertainty))
+			return false;
+		if (Double.doubleToLongBits(this.value) != Double
+				.doubleToLongBits(other.value))
+			return false;
+		return true;
+	}
+	
+	/**
+	 * @param other another {@code UncertainDouble}
+	 * @return true iff this and {@code other} are within each other's
+	 *         uncertainty range.
+	 * @since 2020-09-07
+	 */
+	public final boolean equivalent(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return Math.abs(this.value - other.value) <= Math.min(this.uncertainty,
+				other.uncertainty);
+	}
+	
+	/**
+	 * Gets the preferred scale for rounding a value for toString.
+	 * 
+	 * @since 2020-09-07
+	 */
+	private final int getDisplayScale() {
+		// round based on uncertainty
+		// if uncertainty starts with 1 (ignoring zeroes and the decimal
+		// point), rounds
+		// so that uncertainty has 2 significant digits.
+		// otherwise, rounds so that uncertainty has 1 significant digits.
+		// the value is rounded to the same number of decimal places as the
+		// uncertainty.
+		final BigDecimal bigUncertainty = BigDecimal.valueOf(this.uncertainty);
+		
+		// the scale that will give the uncertainty two decimal places
+		final int twoDecimalPlacesScale = bigUncertainty.scale()
+				- bigUncertainty.precision() + 2;
+		final BigDecimal roundedUncertainty = bigUncertainty
+				.setScale(twoDecimalPlacesScale, RoundingMode.HALF_EVEN);
+		
+		if (roundedUncertainty.unscaledValue().intValue() >= 20)
+			return twoDecimalPlacesScale - 1; // one decimal place
+		else
+			return twoDecimalPlacesScale;
+	}
+	
+	@Override
+	public final int hashCode() {
+		final int prime = 31;
+		int result = 1;
+		long temp;
+		temp = Double.doubleToLongBits(this.uncertainty);
+		result = prime * result + (int) (temp ^ temp >>> 32);
+		temp = Double.doubleToLongBits(this.value);
+		result = prime * result + (int) (temp ^ temp >>> 32);
+		return result;
+	}
+	
+	/**
+	 * @return true iff the value has no uncertainty
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final boolean isExact() {
+		return this.uncertainty == 0;
+	}
+	
+	/**
+	 * Returns the difference of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble minus(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.of(this.value - other.value,
+				Math.hypot(this.uncertainty, other.uncertainty));
+	}
+	
+	/**
+	 * Returns the difference of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble minusExact(double other) {
+		return UncertainDouble.of(this.value - other, this.uncertainty);
+	}
+	
+	/**
+	 * Returns the sum of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble plus(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.of(this.value + other.value,
+				Math.hypot(this.uncertainty, other.uncertainty));
+	}
+	
+	/**
+	 * Returns the sum of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble plusExact(double other) {
+		return UncertainDouble.of(this.value + other, this.uncertainty);
+	}
+	
+	/**
+	 * @return relative uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double relativeUncertainty() {
+		return this.uncertainty / this.value;
+	}
+	
+	/**
+	 * Returns the product of {@code this} and {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble times(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		return UncertainDouble.ofRelative(this.value * other.value, Math
+				.hypot(this.relativeUncertainty(), other.relativeUncertainty()));
+	}
+	
+	/**
+	 * Returns the product of {@code this} and the exact value {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble timesExact(double other) {
+		return UncertainDouble.of(this.value * other, this.uncertainty * other);
+	}
+	
+	/**
+	 * Returns the result of {@code this} raised to the exponent {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble toExponent(UncertainDouble other) {
+		Objects.requireNonNull(other, "other may not be null");
+		
+		final double result = Math.pow(this.value, other.value);
+		final double relativeUncertainty = Math.hypot(
+				other.value * this.relativeUncertainty(),
+				Math.log(this.value) * other.uncertainty);
+		
+		return UncertainDouble.ofRelative(result, relativeUncertainty);
+	}
+	
+	/**
+	 * Returns the result of {@code this} raised the exact exponent
+	 * {@code other}.
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final UncertainDouble toExponentExact(double other) {
+		return UncertainDouble.ofRelative(Math.pow(this.value, other),
+				this.relativeUncertainty() * other);
+	}
+	
+	/**
+	 * Returns a string representation of this {@code UncertainDouble}.
+	 * <p>
+	 * This method returns the same value as {@link #toString(boolean)}, but
+	 * {@code showUncertainty} is true if and only if the uncertainty is
+	 * non-zero.
+	 * 
+	 * <p>
+	 * Examples:
+	 * 
+	 * <pre>
+	 * UncertainDouble.of(3.27, 0.22).toString() = "3.3 ± 0.2"
+	 * UncertainDouble.of(3.27, 0.13).toString() = "3.27 ± 0.13"
+	 * UncertainDouble.of(-5.01, 0).toString() = "-5.01"
+	 * </pre>
+	 * 
+	 * @since 2020-09-07
+	 */
+	@Override
+	public final String toString() {
+		return this.toString(!this.isExact());
+	}
+	
+	/**
+	 * Returns a string representation of this {@code UncertainDouble}.
+	 * <p>
+	 * If {@code showUncertainty} is true, the string will be of the form "VALUE
+	 * ± UNCERTAINTY", and if it is false the string will be of the form "VALUE"
+	 * <p>
+	 * VALUE represents a string representation of this {@code UncertainDouble}'s
+	 * value. If the uncertainty is non-zero, the string will be rounded to the
+	 * same precision as the uncertainty, otherwise it will not be rounded. The
+	 * string is still rounded if {@code showUncertainty} is false.<br>
+	 * UNCERTAINTY represents a string representation of this
+	 * {@code UncertainDouble}'s uncertainty. If the uncertainty ends in 1X
+	 * (where X represents any digit) it will be rounded to two significant
+	 * digits otherwise it will be rounded to one significant digit.
+	 * <p>
+	 * Examples:
+	 * 
+	 * <pre>
+	 * UncertainDouble.of(3.27, 0.22).toString(false) = "3.3"
+	 * UncertainDouble.of(3.27, 0.22).toString(true) = "3.3 ± 0.2"
+	 * UncertainDouble.of(3.27, 0.13).toString(false) = "3.27"
+	 * UncertainDouble.of(3.27, 0.13).toString(true) = "3.27 ± 0.13"
+	 * UncertainDouble.of(-5.01, 0).toString(false) = "-5.01"
+	 * UncertainDouble.of(-5.01, 0).toString(true) = "-5.01 ± 0.0"
+	 * </pre>
+	 * 
+	 * @since 2020-09-07
+	 */
+	public final String toString(boolean showUncertainty) {
+		String valueString, uncertaintyString;
+		
+		// generate the string representation of value and uncertainty
+		if (this.isExact()) {
+			uncertaintyString = "0.0";
+			valueString = Double.toString(this.value);
+			
+		} else {
+			// round the value and uncertainty according to getDisplayScale()
+			final BigDecimal bigValue = BigDecimal.valueOf(this.value);
+			final BigDecimal bigUncertainty = BigDecimal.valueOf(this.uncertainty);
+			
+			final int displayScale = this.getDisplayScale();
+			final BigDecimal roundedUncertainty = bigUncertainty
+					.setScale(displayScale, RoundingMode.HALF_EVEN);
+			final BigDecimal roundedValue = bigValue.setScale(displayScale,
+					RoundingMode.HALF_EVEN);
+			
+			valueString = roundedValue.toString();
+			uncertaintyString = roundedUncertainty.toString();
+		}
+		
+		// return "value" or "value ± uncertainty" depending on showUncertainty
+		return valueString + (showUncertainty ? " ± " + uncertaintyString : "");
+	}
+	
+	/**
+	 * @return absolute uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double uncertainty() {
+		return this.uncertainty;
+	}
+	
+	/**
+	 * @return value without uncertainty
+	 * @since 2020-09-07
+	 */
+	public final double value() {
+		return this.value;
+	}
+}
diff --git a/src/org/unitConverter/unit/LinearUnit.java b/src/org/unitConverter/unit/LinearUnit.java
index 762572a..2d63ca7 100644
--- a/src/org/unitConverter/unit/LinearUnit.java
+++ b/src/org/unitConverter/unit/LinearUnit.java
@@ -20,89 +20,83 @@ import java.util.Objects;
 
 import org.unitConverter.math.DecimalComparison;
 import org.unitConverter.math.ObjectProduct;
+import org.unitConverter.math.UncertainDouble;
 
 /**
- * A unit that can be expressed as a product of its base and a number. For example, kilometres, inches and pounds.
+ * A unit that can be expressed as a product of its base and a number. For
+ * example, kilometres, inches and pounds.
  * 
  * @author Adrien Hopkins
  * @since 2019-10-16
  */
 public final class LinearUnit extends Unit {
 	/**
-	 * Gets a {@code LinearUnit} from a unit and a value. For example, converts '59 °F' to a linear unit with the value
-	 * of '288.15 K'
+	 * Gets a {@code LinearUnit} from a unit and a value. For example, converts
+	 * '59 °F' to a linear unit with the value of '288.15 K'
 	 * 
-	 * @param unit
-	 *            unit to convert
-	 * @param value
-	 *            value to convert
+	 * @param unit  unit to convert
+	 * @param value value to convert
 	 * @return value expressed as a {@code LinearUnit}
 	 * @since 2019-10-16
-	 * @throws NullPointerException
-	 *             if unit is null
+	 * @throws NullPointerException if unit is null
 	 */
 	public static LinearUnit fromUnitValue(final Unit unit, final double value) {
-		return new LinearUnit(Objects.requireNonNull(unit, "unit must not be null.").getBase(),
+		return new LinearUnit(
+				Objects.requireNonNull(unit, "unit must not be null.").getBase(),
 				unit.convertToBase(value), NameSymbol.EMPTY);
 	}
-
+	
 	/**
-	 * Gets a {@code LinearUnit} from a unit and a value. For example, converts '59 °F' to a linear unit with the value
-	 * of '288.15 K'
+	 * Gets a {@code LinearUnit} from a unit and a value. For example, converts
+	 * '59 °F' to a linear unit with the value of '288.15 K'
 	 * 
-	 * @param unit
-	 *            unit to convert
-	 * @param value
-	 *            value to convert
-	 * @param ns
-	 *            name(s) and symbol of unit
+	 * @param unit  unit to convert
+	 * @param value value to convert
+	 * @param ns    name(s) and symbol of unit
 	 * @return value expressed as a {@code LinearUnit}
 	 * @since 2019-10-21
-	 * @throws NullPointerException
-	 *             if unit or ns is null
+	 * @throws NullPointerException if unit or ns is null
 	 */
-	public static LinearUnit fromUnitValue(final Unit unit, final double value, final NameSymbol ns) {
-		return new LinearUnit(Objects.requireNonNull(unit, "unit must not be null.").getBase(),
+	public static LinearUnit fromUnitValue(final Unit unit, final double value,
+			final NameSymbol ns) {
+		return new LinearUnit(
+				Objects.requireNonNull(unit, "unit must not be null.").getBase(),
 				unit.convertToBase(value), ns);
 	}
-
+	
 	/**
-	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In other words, gets the product of
-	 * {@code unitBase} and {@code conversionFactor}, expressed as a {@code LinearUnit}.
+	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In
+	 * other words, gets the product of {@code unitBase} and
+	 * {@code conversionFactor}, expressed as a {@code LinearUnit}.
 	 * 
-	 * @param unitBase
-	 *            unit base to multiply by
-	 * @param conversionFactor
-	 *            number to multiply base by
+	 * @param unitBase         unit base to multiply by
+	 * @param conversionFactor number to multiply base by
 	 * @return product of base and conversion factor
 	 * @since 2019-10-16
-	 * @throws NullPointerException
-	 *             if unitBase is null
+	 * @throws NullPointerException if unitBase is null
 	 */
-	public static LinearUnit valueOf(final ObjectProduct<BaseUnit> unitBase, final double conversionFactor) {
+	public static LinearUnit valueOf(final ObjectProduct<BaseUnit> unitBase,
+			final double conversionFactor) {
 		return new LinearUnit(unitBase, conversionFactor, NameSymbol.EMPTY);
 	}
-
+	
 	/**
-	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In other words, gets the product of
-	 * {@code unitBase} and {@code conversionFactor}, expressed as a {@code LinearUnit}.
+	 * Gets a {@code LinearUnit} from a unit base and a conversion factor. In
+	 * other words, gets the product of {@code unitBase} and
+	 * {@code conversionFactor}, expressed as a {@code LinearUnit}.
 	 * 
-	 * @param unitBase
-	 *            unit base to multiply by
-	 * @param conversionFactor
-	 *            number to multiply base by
-	 * @param ns
-	 *            name(s) and symbol of unit
+	 * @param unitBase         unit base to multiply by
+	 * @param conversionFactor number to multiply base by
+	 * @param ns               name(s) and symbol of unit
 	 * @return product of base and conversion factor
 	 * @since 2019-10-21
-	 * @throws NullPointerException
-	 *             if unitBase is null
+	 * @throws NullPointerException if unitBase is null
 	 */
-	public static LinearUnit valueOf(final ObjectProduct<BaseUnit> unitBase, final double conversionFactor,
-			final NameSymbol ns) {
+	public static LinearUnit valueOf(final ObjectProduct<BaseUnit> unitBase,
+			final double conversionFactor, final NameSymbol ns) {
 		return new LinearUnit(unitBase, conversionFactor, ns);
 	}
-
+	
 	/**
 	 * The value of this unit as represented in its base form. Mathematically,
 	 * 
@@ -113,21 +107,20 @@ public final class LinearUnit extends Unit {
 	 * @since 2019-10-16
 	 */
 	private final double conversionFactor;
-
+	
 	/**
 	 * Creates the {@code LinearUnit}.
 	 * 
-	 * @param unitBase
-	 *            base of linear unit
-	 * @param conversionFactor
-	 *            conversion factor between base and unit
+	 * @param unitBase         base of linear unit
+	 * @param conversionFactor conversion factor between base and unit
 	 * @since 2019-10-16
 	 */
-	private LinearUnit(final ObjectProduct<BaseUnit> unitBase, final double conversionFactor, final NameSymbol ns) {
+	private LinearUnit(final ObjectProduct<BaseUnit> unitBase,
+			final double conversionFactor, final NameSymbol ns) {
 		super(unitBase, ns);
 		this.conversionFactor = conversionFactor;
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -137,7 +130,32 @@ public final class LinearUnit extends Unit {
 	protected double convertFromBase(final double value) {
 		return value / this.getConversionFactor();
 	}
-
+	
+	/**
+	 * Converts an {@code UncertainDouble} value expressed in this unit to an
+	 * {@code UncertainValue} value expressed in {@code other}.
+	 * 
+	 * @param other unit to convert to
+	 * @param value value to convert
+	 * @return converted value
+	 * @since 2019-09-07
+	 * @throws IllegalArgumentException if {@code other} is incompatible for
+	 *                                  conversion with this unit (as tested by
+	 *                                  {@link Unit#canConvertTo}).
+	 * @throws NullPointerException     if value or other is null
+	 */
+	public UncertainDouble convertTo(LinearUnit other, UncertainDouble value) {
+		Objects.requireNonNull(other, "other must not be null.");
+		Objects.requireNonNull(value, "value may not be null.");
+		if (this.canConvertTo(other))
+			return value.timesExact(
+					this.getConversionFactor() / other.getConversionFactor());
+		else
+			throw new IllegalArgumentException(
+					String.format("Cannot convert from %s to %s.", this, other));
+		
+	}
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -147,12 +165,20 @@ public final class LinearUnit extends Unit {
 	protected double convertToBase(final double value) {
 		return value * this.getConversionFactor();
 	}
-
+	
+	/**
+	 * Converts an {@code UncertainDouble} to the base unit.
+	 * 
+	 * @since 2020-09-07
+	 */
+	UncertainDouble convertToBase(final UncertainDouble value) {
+		return value.timesExact(this.getConversionFactor());
+	}
+	
 	/**
 	 * Divides this unit by a scalar.
 	 * 
-	 * @param divisor
-	 *            scalar to divide by
+	 * @param divisor scalar to divide by
 	 * @return quotient
 	 * @since 2018-12-23
 	 * @since v0.1.0
@@ -160,26 +186,26 @@ public final class LinearUnit extends Unit {
 	public LinearUnit dividedBy(final double divisor) {
 		return valueOf(this.getBase(), this.getConversionFactor() / divisor);
 	}
-
+	
 	/**
 	 * Returns the quotient of this unit and another.
 	 * 
-	 * @param divisor
-	 *            unit to divide by
+	 * @param divisor unit to divide by
 	 * @return quotient of two units
-	 * @throws NullPointerException
-	 *             if {@code divisor} is null
+	 * @throws NullPointerException if {@code divisor} is null
 	 * @since 2018-12-22
 	 * @since v0.1.0
 	 */
 	public LinearUnit dividedBy(final LinearUnit divisor) {
 		Objects.requireNonNull(divisor, "other must not be null");
-
+		
 		// divide the units
-		final ObjectProduct<BaseUnit> base = this.getBase().dividedBy(divisor.getBase());
-		return valueOf(base, this.getConversionFactor() / divisor.getConversionFactor());
+		final ObjectProduct<BaseUnit> base = this.getBase()
+				.dividedBy(divisor.getBase());
+		return valueOf(base,
+				this.getConversionFactor() / divisor.getConversionFactor());
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -191,9 +217,10 @@ public final class LinearUnit extends Unit {
 			return false;
 		final LinearUnit other = (LinearUnit) obj;
 		return Objects.equals(this.getBase(), other.getBase())
-				&& DecimalComparison.equals(this.getConversionFactor(), other.getConversionFactor());
+				&& DecimalComparison.equals(this.getConversionFactor(),
+						other.getConversionFactor());
 	}
-
+	
 	/**
 	 * @return conversion factor
 	 * @since 2019-10-16
@@ -201,7 +228,7 @@ public final class LinearUnit extends Unit {
 	public double getConversionFactor() {
 		return this.conversionFactor;
 	}
-
+	
 	/**
 	 * {@inheritDoc}
 	 * 
@@ -209,18 +236,20 @@ public final class LinearUnit extends Unit {
 	 */
 	@Override
 	public int hashCode() {
-		return 31 * this.getBase().hashCode() + DecimalComparison.hash(this.getConversionFactor());
+		return 31 * this.getBase().hashCode()
+				+ DecimalComparison.hash(this.getConversionFactor());
 	}
-
+	
 	/**
-	 * @return whether this unit is equivalent to a {@code BaseUnit} (i.e. there is a {@code BaseUnit b} where
+	 * @return whether this unit is equivalent to a {@code BaseUnit} (i.e. there
+	 *         is a {@code BaseUnit b} where
 	 *         {@code b.asLinearUnit().equals(this)} returns {@code true}.)
 	 * @since 2019-10-16
 	 */
 	public boolean isBase() {
 		return this.isCoherent() && this.getBase().isSingleObject();
 	}
-
+	
 	/**
 	 * @return whether this unit is coherent (i.e. has conversion factor 1)
 	 * @since 2019-10-16
@@ -228,70 +257,73 @@ public final class LinearUnit extends Unit {
 	public boolean isCoherent() {
 		return this.getConversionFactor() == 1;
 	}
-
+	
 	/**
 	 * Returns the difference of this unit and another.
 	 * <p>
-	 * Two units can be subtracted if they have the same base. Note that {@link #canConvertTo} can be used to determine
-	 * this. If {@code subtrahend} does not meet this condition, an {@code IllegalArgumentException} will be thrown.
+	 * Two units can be subtracted if they have the same base. Note that
+	 * {@link #canConvertTo} can be used to determine this. If {@code subtrahend}
+	 * does not meet this condition, an {@code IllegalArgumentException} will be
+	 * thrown.
 	 * </p>
 	 * 
-	 * @param subtrahend
-	 *            unit to subtract
+	 * @param subtrahend unit to subtract
 	 * @return difference of units
-	 * @throws IllegalArgumentException
-	 *             if {@code subtrahend} is not compatible for subtraction as described above
-	 * @throws NullPointerException
-	 *             if {@code subtrahend} is null
+	 * @throws IllegalArgumentException if {@code subtrahend} is not compatible
+	 *                                  for subtraction as described above
+	 * @throws NullPointerException     if {@code subtrahend} is null
 	 * @since 2019-03-17
 	 * @since v0.2.0
 	 */
 	public LinearUnit minus(final LinearUnit subtrahend) {
 		Objects.requireNonNull(subtrahend, "addend must not be null.");
-
+		
 		// reject subtrahends that cannot be added to this unit
 		if (!this.getBase().equals(subtrahend.getBase()))
-			throw new IllegalArgumentException(
-					String.format("Incompatible units for subtraction \"%s\" and \"%s\".", this, subtrahend));
-
+			throw new IllegalArgumentException(String.format(
+					"Incompatible units for subtraction \"%s\" and \"%s\".", this,
+					subtrahend));
+		
 		// subtract the units
-		return valueOf(this.getBase(), this.getConversionFactor() - subtrahend.getConversionFactor());
+		return valueOf(this.getBase(),
+				this.getConversionFactor() - subtrahend.getConversionFactor());
 	}
-
+	
 	/**
 	 * Returns the sum of this unit and another.
 	 * <p>
-	 * Two units can be added if they have the same base. Note that {@link #canConvertTo} can be used to determine this.
-	 * If {@code addend} does not meet this condition, an {@code IllegalArgumentException} will be thrown.
+	 * Two units can be added if they have the same base. Note that
+	 * {@link #canConvertTo} can be used to determine this. If {@code addend}
+	 * does not meet this condition, an {@code IllegalArgumentException} will be
+	 * thrown.
 	 * </p>
 	 * 
-	 * @param addend
-	 *            unit to add
+	 * @param addend unit to add
 	 * @return sum of units
-	 * @throws IllegalArgumentException
-	 *             if {@code addend} is not compatible for addition as described above
-	 * @throws NullPointerException
-	 *             if {@code addend} is null
+	 * @throws IllegalArgumentException if {@code addend} is not compatible for
+	 *                                  addition as described above
+	 * @throws NullPointerException     if {@code addend} is null
 	 * @since 2019-03-17
 	 * @since v0.2.0
 	 */
 	public LinearUnit plus(final LinearUnit addend) {
 		Objects.requireNonNull(addend, "addend must not be null.");
-
+		
 		// reject addends that cannot be added to this unit
 		if (!this.getBase().equals(addend.getBase()))
-			throw new IllegalArgumentException(
-					String.format("Incompatible units for addition \"%s\" and \"%s\".", this, addend));
-
+			throw new IllegalArgumentException(String.format(
+					"Incompatible units for addition \"%s\" and \"%s\".", this,
+					addend));
+		
 		// add the units
-		return valueOf(this.getBase(), this.getConversionFactor() + addend.getConversionFactor());
+		return valueOf(this.getBase(),
+				this.getConversionFactor() + addend.getConversionFactor());
 	}
-
+	
 	/**
 	 * Multiplies this unit by a scalar.
 	 * 
-	 * @param multiplier
-	 *            scalar to multiply by
+	 * @param multiplier scalar to multiply by
 	 * @return product
 	 * @since 2018-12-23
 	 * @since v0.1.0
@@ -299,39 +331,39 @@ public final class LinearUnit extends Unit {
 	public LinearUnit times(final double multiplier) {
 		return valueOf(this.getBase(), this.getConversionFactor() * multiplier);
 	}
-
+	
 	/**
 	 * Returns the product of this unit and another.
 	 * 
-	 * @param multiplier
-	 *            unit to multiply by
+	 * @param multiplier unit to multiply by
 	 * @return product of two units
-	 * @throws NullPointerException
-	 *             if {@code multiplier} is null
+	 * @throws NullPointerException if {@code multiplier} is null
 	 * @since 2018-12-22
 	 * @since v0.1.0
 	 */
 	public LinearUnit times(final LinearUnit multiplier) {
 		Objects.requireNonNull(multiplier, "other must not be null");
-
+		
 		// multiply the units
-		final ObjectProduct<BaseUnit> base = this.getBase().times(multiplier.getBase());
-		return valueOf(base, this.getConversionFactor() * multiplier.getConversionFactor());
+		final ObjectProduct<BaseUnit> base = this.getBase()
+				.times(multiplier.getBase());
+		return valueOf(base,
+				this.getConversionFactor() * multiplier.getConversionFactor());
 	}
-
+	
 	/**
 	 * Returns this unit but to an exponent.
 	 * 
-	 * @param exponent
-	 *            exponent to exponentiate unit to
+	 * @param exponent exponent to exponentiate unit to
 	 * @return exponentiated unit
 	 * @since 2019-01-15
 	 * @since v0.1.0
 	 */
 	public LinearUnit toExponent(final int exponent) {
-		return valueOf(this.getBase().toExponent(exponent), Math.pow(this.conversionFactor, exponent));
+		return valueOf(this.getBase().toExponent(exponent),
+				Math.pow(this.conversionFactor, exponent));
 	}
-
+	
 	/**
 	 * @return a string providing a definition of this unit
 	 * @since 2019-10-21
@@ -339,10 +371,13 @@ public final class LinearUnit extends Unit {
 	@Override
 	public String toString() {
 		return this.getPrimaryName().orElse("Unnamed unit")
-				+ (this.getSymbol().isPresent() ? String.format(" (%s)", this.getSymbol().get()) : "") + ", "
-				+ Double.toString(this.conversionFactor) + " * " + this.getBase().toString(u -> u.getSymbol().get());
+				+ (this.getSymbol().isPresent()
+						? String.format(" (%s)", this.getSymbol().get())
+						: "")
+				+ ", " + Double.toString(this.conversionFactor) + " * "
+				+ this.getBase().toString(u -> u.getSymbol().get());
 	}
-
+	
 	@Override
 	public LinearUnit withName(final NameSymbol ns) {
 		return valueOf(this.getBase(), this.getConversionFactor(), ns);
@@ -351,37 +386,38 @@ public final class LinearUnit extends Unit {
 	/**
 	 * Returns the result of applying {@code prefix} to this unit.
 	 * <p>
-	 * If this unit and the provided prefix have a primary name, the returned unit will have a primary name (prefix's
-	 * name + unit's name). <br>
-	 * If this unit and the provided prefix have a symbol, the returned unit will have a symbol. <br>
-	 * This method ignores alternate names of both this unit and the provided prefix.
+	 * If this unit and the provided prefix have a primary name, the returned
+	 * unit will have a primary name (prefix's name + unit's name). <br>
+	 * If this unit and the provided prefix have a symbol, the returned unit will
+	 * have a symbol. <br>
+	 * This method ignores alternate names of both this unit and the provided
+	 * prefix.
 	 * 
-	 * @param prefix
-	 *            prefix to apply
+	 * @param prefix prefix to apply
 	 * @return unit with prefix
 	 * @since 2019-03-18
 	 * @since v0.2.0
-	 * @throws NullPointerException
-	 *             if prefix is null
+	 * @throws NullPointerException if prefix is null
 	 */
 	public LinearUnit withPrefix(final UnitPrefix prefix) {
 		final LinearUnit unit = this.times(prefix.getMultiplier());
-
+		
 		// create new name and symbol, if possible
 		final String name;
-		if (this.getPrimaryName().isPresent() && prefix.getPrimaryName().isPresent()) {
+		if (this.getPrimaryName().isPresent()
+				&& prefix.getPrimaryName().isPresent()) {
 			name = prefix.getPrimaryName().get() + this.getPrimaryName().get();
 		} else {
 			name = null;
 		}
-
+		
 		final String symbol;
 		if (this.getSymbol().isPresent() && prefix.getSymbol().isPresent()) {
 			symbol = prefix.getSymbol().get() + this.getSymbol().get();
 		} else {
 			symbol = null;
 		}
-
+		
 		return unit.withName(NameSymbol.ofNullable(name, symbol));
 	}
 }
diff --git a/src/org/unitConverter/unit/LinearUnitValue.java b/src/org/unitConverter/unit/LinearUnitValue.java
index 5685a6d..d86d344 100644
--- a/src/org/unitConverter/unit/LinearUnitValue.java
+++ b/src/org/unitConverter/unit/LinearUnitValue.java
@@ -3,12 +3,11 @@
  */
 package org.unitConverter.unit;
 
-import java.math.BigDecimal;
-import java.math.RoundingMode;
 import java.util.Objects;
 import java.util.Optional;
 
 import org.unitConverter.math.DecimalComparison;
+import org.unitConverter.math.UncertainDouble;
 
 /**
  * A possibly uncertain value expressed in a linear unit.
@@ -33,7 +32,8 @@ public final class LinearUnitValue {
 	public static final LinearUnitValue getExact(final LinearUnit unit,
 			final double value) {
 		return new LinearUnitValue(
-				Objects.requireNonNull(unit, "unit must not be null"), value, 0);
+				Objects.requireNonNull(unit, "unit must not be null"),
+				UncertainDouble.of(value, 0));
 	}
 	
 	/**
@@ -46,41 +46,23 @@ public final class LinearUnitValue {
 	 * @since 2020-07-26
 	 */
 	public static final LinearUnitValue of(final LinearUnit unit,
-			final double value, final double uncertainty) {
+			final UncertainDouble value) {
 		return new LinearUnitValue(
-				Objects.requireNonNull(unit, "unit must not be null"), value,
-				uncertainty);
-	}
-	
-	/**
-	 * Gets an uncertain {@code LinearUnitValue}
-	 * 
-	 * @param unit                unit to express with
-	 * @param value               value to express
-	 * @param relativeUncertainty relative uncertainty of value
-	 * @return uncertain {@code LinearUnitValue} instance
-	 * @since 2020-07-28
-	 */
-	public static final LinearUnitValue ofRelative(final LinearUnit unit,
-			final double value, final double relativeUncertainty) {
-		return LinearUnitValue.of(unit, value, relativeUncertainty * value);
+				Objects.requireNonNull(unit, "unit must not be null"),
+				Objects.requireNonNull(value, "value may not be null"));
 	}
 	
 	private final LinearUnit unit;
-	private final double value;
-	private final double uncertainty;
+	private final UncertainDouble value;
 	
 	/**
-	 * @param unit        unit to express as
-	 * @param value       value to express
-	 * @param uncertainty absolute uncertainty of value
+	 * @param unit  unit to express as
+	 * @param value value to express
 	 * @since 2020-07-26
 	 */
-	private LinearUnitValue(final LinearUnit unit, final double value,
-			final double uncertainty) {
+	private LinearUnitValue(final LinearUnit unit, final UncertainDouble value) {
 		this.unit = unit;
 		this.value = value;
-		this.uncertainty = uncertainty;
 	}
 	
 	/**
@@ -89,7 +71,7 @@ public final class LinearUnitValue {
 	 * @since 2020-08-04
 	 */
 	public final UnitValue asUnitValue() {
-		return UnitValue.of(this.unit, this.value);
+		return UnitValue.of(this.unit, this.value.value());
 	}
 	
 	/**
@@ -110,8 +92,7 @@ public final class LinearUnitValue {
 	 * @since 2020-07-26
 	 */
 	public final LinearUnitValue convertTo(final LinearUnit other) {
-		return LinearUnitValue.of(other, this.unit.convertTo(other, this.value),
-				this.unit.convertTo(other, this.uncertainty));
+		return LinearUnitValue.of(other, this.unit.convertTo(other, this.value));
 	}
 	
 	/**
@@ -122,8 +103,7 @@ public final class LinearUnitValue {
 	 * @since 2020-07-28
 	 */
 	public LinearUnitValue dividedBy(final double divisor) {
-		return LinearUnitValue.of(this.unit, this.value / divisor,
-				this.uncertainty / divisor);
+		return LinearUnitValue.of(this.unit, this.value.dividedByExact(divisor));
 	}
 	
 	/**
@@ -134,10 +114,8 @@ public final class LinearUnitValue {
 	 * @since 2020-07-28
 	 */
 	public LinearUnitValue dividedBy(final LinearUnitValue divisor) {
-		return LinearUnitValue.ofRelative(this.unit.dividedBy(divisor.unit),
-				this.value / divisor.value,
-				Math.hypot(this.getRelativeUncertainty(),
-						divisor.getRelativeUncertainty()));
+		return LinearUnitValue.of(this.unit.dividedBy(divisor.unit),
+				this.value.dividedBy(divisor.value));
 	}
 	
 	/**
@@ -154,12 +132,8 @@ public final class LinearUnitValue {
 			return false;
 		final LinearUnitValue other = (LinearUnitValue) obj;
 		return Objects.equals(this.unit.getBase(), other.unit.getBase())
-				&& Double.doubleToLongBits(
-						this.unit.convertToBase(this.getValue())) == Double
-								.doubleToLongBits(
-										other.unit.convertToBase(other.getValue()))
-				&& Double.doubleToLongBits(this.getRelativeUncertainty()) == Double
-						.doubleToLongBits(other.getRelativeUncertainty());
+				&& this.unit.convertToBase(this.value)
+						.equals(other.unit.convertToBase(other.value));
 	}
 	
 	/**
@@ -180,9 +154,7 @@ public final class LinearUnitValue {
 		final LinearUnitValue other = (LinearUnitValue) obj;
 		return Objects.equals(this.unit.getBase(), other.unit.getBase())
 				&& DecimalComparison.equals(this.unit.convertToBase(this.value),
-						other.unit.convertToBase(other.value))
-				&& DecimalComparison.equals(this.getRelativeUncertainty(),
-						other.getRelativeUncertainty());
+						other.unit.convertToBase(other.value));
 	}
 	
 	/**
@@ -195,32 +167,11 @@ public final class LinearUnitValue {
 		if (other == null
 				|| !Objects.equals(this.unit.getBase(), other.unit.getBase()))
 			return false;
-		final double thisBaseValue = this.unit.convertToBase(this.value);
-		final double otherBaseValue = other.unit.convertToBase(other.value);
-		final double thisBaseUncertainty = this.unit
-				.convertToBase(this.uncertainty);
-		final double otherBaseUncertainty = other.unit
-				.convertToBase(other.uncertainty);
-		return Math.abs(thisBaseValue - otherBaseValue) <= Math
-				.min(thisBaseUncertainty, otherBaseUncertainty);
-	}
-	
-	/**
-	 * @return relative uncertainty of value
-	 * 
-	 * @since 2020-07-26
-	 */
-	public final double getRelativeUncertainty() {
-		return this.uncertainty / this.value;
-	}
-	
-	/**
-	 * @return absolute uncertainty of value
-	 * 
-	 * @since 2020-07-26
-	 */
-	public final double getUncertainty() {
-		return this.uncertainty;
+		final LinearUnit base = LinearUnit.valueOf(this.unit.getBase(), 1);
+		final LinearUnitValue thisBase = this.convertTo(base);
+		final LinearUnitValue otherBase = other.convertTo(base);
+		
+		return thisBase.value.equivalent(otherBase.value);
 	}
 	
 	/**
@@ -237,24 +188,22 @@ public final class LinearUnitValue {
 	 * 
 	 * @since 2020-07-26
 	 */
-	public final double getValue() {
+	public final UncertainDouble getValue() {
 		return this.value;
 	}
 	
+	/**
+	 * @return the exact value
+	 * @since 2020-09-07
+	 */
+	public final double getValueExact() {
+		return this.value.value();
+	}
+	
 	@Override
 	public int hashCode() {
 		return Objects.hash(this.unit.getBase(),
-				this.unit.convertToBase(this.getValue()),
-				this.getRelativeUncertainty());
-	}
-	
-	/**
-	 * @return true iff the value has no uncertainty
-	 * 
-	 * @since 2020-07-26
-	 */
-	public final boolean isExact() {
-		return this.uncertainty == 0;
+				this.unit.convertToBase(this.getValue()));
 	}
 	
 	/**
@@ -276,8 +225,8 @@ public final class LinearUnitValue {
 					this.unit, subtrahend.unit));
 		
 		final LinearUnitValue otherConverted = subtrahend.convertTo(this.unit);
-		return LinearUnitValue.of(this.unit, this.value - otherConverted.value,
-				Math.hypot(this.uncertainty, otherConverted.uncertainty));
+		return LinearUnitValue.of(this.unit,
+				this.value.minus(otherConverted.value));
 	}
 	
 	/**
@@ -298,8 +247,8 @@ public final class LinearUnitValue {
 					addend.unit));
 		
 		final LinearUnitValue otherConverted = addend.convertTo(this.unit);
-		return LinearUnitValue.of(this.unit, this.value + otherConverted.value,
-				Math.hypot(this.uncertainty, otherConverted.uncertainty));
+		return LinearUnitValue.of(this.unit,
+				this.value.plus(otherConverted.value));
 	}
 	
 	/**
@@ -310,8 +259,7 @@ public final class LinearUnitValue {
 	 * @since 2020-07-28
 	 */
 	public LinearUnitValue times(final double multiplier) {
-		return LinearUnitValue.of(this.unit, this.value * multiplier,
-				this.uncertainty * multiplier);
+		return LinearUnitValue.of(this.unit, this.value.timesExact(multiplier));
 	}
 	
 	/**
@@ -322,10 +270,8 @@ public final class LinearUnitValue {
 	 * @since 2020-07-28
 	 */
 	public LinearUnitValue times(final LinearUnitValue multiplier) {
-		return LinearUnitValue.ofRelative(this.unit.times(multiplier.unit),
-				this.value * multiplier.value,
-				Math.hypot(this.getRelativeUncertainty(),
-						multiplier.getRelativeUncertainty()));
+		return LinearUnitValue.of(this.unit.times(multiplier.unit),
+				this.value.times(multiplier.value));
 	}
 	
 	/**
@@ -336,14 +282,13 @@ public final class LinearUnitValue {
 	 * @since 2020-07-28
 	 */
 	public LinearUnitValue toExponent(final int exponent) {
-		return LinearUnitValue.ofRelative(this.unit.toExponent(exponent),
-				Math.pow(this.value, exponent),
-				this.getRelativeUncertainty() * Math.sqrt(exponent));
+		return LinearUnitValue.of(this.unit.toExponent(exponent),
+				this.value.toExponentExact(exponent));
 	}
 	
 	@Override
 	public String toString() {
-		return this.toString(!this.isExact());
+		return this.toString(!this.value.isExact());
 	}
 	
 	/**
@@ -363,107 +308,22 @@ public final class LinearUnitValue {
 		final Optional<String> symbol = this.unit.getSymbol();
 		final String chosenName = symbol.orElse(primaryName.orElse(null));
 		
-		final double baseValue = this.unit.convertToBase(this.value);
-		final double baseUncertainty = this.unit.convertToBase(this.uncertainty);
+		final UncertainDouble baseValue = this.unit.convertToBase(this.value);
 		
 		// get rounded strings
-		String valueString, baseValueString, uncertaintyString,
-				baseUncertaintyString;
-		if (this.isExact()) {
-			valueString = Double.toString(this.value);
-			baseValueString = Double.toString(baseValue);
-			uncertaintyString = "0";
-			baseUncertaintyString = "0";
-		} else {
-			final BigDecimal bigValue = BigDecimal.valueOf(this.value);
-			final BigDecimal bigUncertainty = BigDecimal.valueOf(this.uncertainty);
-			
-			// round based on uncertainty
-			// if uncertainty starts with 1 (ignoring zeroes and the decimal
-			// point), rounds
-			// so that uncertainty has 2 significant digits.
-			// otherwise, rounds so that uncertainty has 1 significant digits.
-			// the value is rounded to the same number of decimal places as the
-			// uncertainty.
-			BigDecimal roundedUncertainty = bigUncertainty.setScale(
-					bigUncertainty.scale() - bigUncertainty.precision() + 2,
-					RoundingMode.HALF_EVEN);
-			if (roundedUncertainty.unscaledValue().intValue() >= 20) {
-				roundedUncertainty = bigUncertainty.setScale(
-						bigUncertainty.scale() - bigUncertainty.precision() + 1,
-						RoundingMode.HALF_EVEN);
-			}
-			final BigDecimal roundedValue = bigValue
-					.setScale(roundedUncertainty.scale(), RoundingMode.HALF_EVEN);
-			
-			valueString = roundedValue.toString();
-			uncertaintyString = roundedUncertainty.toString();
-			
-			if (primaryName.isEmpty() && symbol.isEmpty()) {
-				final BigDecimal bigBaseValue = BigDecimal.valueOf(baseValue);
-				final BigDecimal bigBaseUncertainty = BigDecimal
-						.valueOf(baseUncertainty);
-				
-				BigDecimal roundedBaseUncertainty = bigBaseUncertainty
-						.setScale(
-								bigBaseUncertainty.scale()
-										- bigBaseUncertainty.precision() + 2,
-								RoundingMode.HALF_EVEN);
-				if (roundedBaseUncertainty.unscaledValue().intValue() >= 20) {
-					roundedBaseUncertainty = bigBaseUncertainty
-							.setScale(
-									bigBaseUncertainty.scale()
-											- bigBaseUncertainty.precision() + 1,
-									RoundingMode.HALF_EVEN);
-				}
-				final BigDecimal roundedBaseValue = bigBaseValue.setScale(
-						roundedBaseUncertainty.scale(), RoundingMode.HALF_EVEN);
-				
-				baseValueString = roundedBaseValue.toString();
-				baseUncertaintyString = roundedBaseUncertainty.toString();
-			} else {
-				// unused
-				baseValueString = "";
-				baseUncertaintyString = "";
-			}
-		}
+		// if showUncertainty is true, add brackets around the string
+		final String valueString = showUncertainty ? "("
+				: "" + this.value.toString(showUncertainty)
+						+ (showUncertainty ? ")" : "");
+		final String baseValueString = showUncertainty ? "("
+				: "" + baseValue.toString(showUncertainty)
+						+ (showUncertainty ? ")" : "");
 		
 		// create string
-		if (showUncertainty) {
-			if (primaryName.isEmpty() && symbol.isEmpty())
-				return String.format("(%s ± %s) unnamed unit (= %s ± %s %s)",
-						valueString, uncertaintyString, baseValueString,
-						baseUncertaintyString, this.unit.getBase());
-			else
-				return String.format("(%s ± %s) %s", valueString, uncertaintyString,
-						chosenName);
-		} else {
-			// truncate excess zeroes
-			if (valueString.contains(".")) {
-				while (valueString.endsWith("0")) {
-					valueString = valueString.substring(0, valueString.length() - 1);
-				}
-				if (valueString.endsWith(".")) {
-					valueString = valueString.substring(0, valueString.length() - 1);
-				}
-			}
-			
-			if (baseValueString.contains(".")) {
-				while (baseValueString.endsWith("0")) {
-					baseValueString = baseValueString.substring(0,
-							baseValueString.length() - 1);
-				}
-				if (baseValueString.endsWith(".")) {
-					baseValueString = baseValueString.substring(0,
-							baseValueString.length() - 1);
-				}
-			}
-			
-			if (primaryName.isEmpty() && symbol.isEmpty())
-				return String.format("%s unnamed unit (= %s %s)", valueString,
-						baseValueString, this.unit.getBase());
-			else
-				return String.format("%s %s", valueString, chosenName);
-		}
+		if (primaryName.isEmpty() && symbol.isEmpty())
+			return String.format("%s unnamed unit (= %s %s)", valueString,
+					baseValueString, this.unit.getBase());
+		else
+			return String.format("%s %s", valueString, chosenName);
 	}
 }
diff --git a/src/org/unitConverter/unit/UnitDatabase.java b/src/org/unitConverter/unit/UnitDatabase.java
index 9812bd0..9ca9617 100644
--- a/src/org/unitConverter/unit/UnitDatabase.java
+++ b/src/org/unitConverter/unit/UnitDatabase.java
@@ -46,6 +46,7 @@ import org.unitConverter.math.ConditionalExistenceCollections;
 import org.unitConverter.math.DecimalComparison;
 import org.unitConverter.math.ExpressionParser;
 import org.unitConverter.math.ObjectProduct;
+import org.unitConverter.math.UncertainDouble;
 
 /**
  * A database of units, prefixes and dimensions, and their names.
@@ -1134,7 +1135,7 @@ public final class UnitDatabase {
 		// exponent function - first check if o2 is a number,
 		if (exponentValue.canConvertTo(SI.ONE)) {
 			// then check if it is an integer,
-			final double exponent = exponentValue.getValue();
+			final double exponent = exponentValue.getValueExact();
 			if (DecimalComparison.equals(exponent % 1, 0))
 				// then exponentiate
 				return base.toExponent((int) (exponent + 0.5));
@@ -1650,7 +1651,8 @@ public final class UnitDatabase {
 			final BigDecimal number = new BigDecimal(name);
 			
 			final double uncertainty = Math.pow(10, -number.scale());
-			return LinearUnitValue.of(SI.ONE, number.doubleValue(), uncertainty);
+			return LinearUnitValue.of(SI.ONE,
+					UncertainDouble.of(number.doubleValue(), uncertainty));
 		} catch (final NumberFormatException e) {
 			return LinearUnitValue.getExact(this.getLinearUnit(name), 1);
 		}
diff --git a/src/org/unitConverter/unit/UnitTest.java b/src/org/unitConverter/unit/UnitTest.java
index ff83805..c0711dc 100644
--- a/src/org/unitConverter/unit/UnitTest.java
+++ b/src/org/unitConverter/unit/UnitTest.java
@@ -56,9 +56,10 @@ class UnitTest {
 		final LinearUnitValue value4 = LinearUnitValue.getExact(SI.KILOGRAM, 60);
 		
 		// make sure addition is done correctly
-		assertEquals(51.576, value1.plus(value2).getValue(), 0.001);
-		assertEquals(15.5, value1.plus(value3).getValue());
-		assertEquals(52.076, value1.plus(value2).plus(value3).getValue(), 0.001);
+		assertEquals(51.576, value1.plus(value2).getValueExact(), 0.001);
+		assertEquals(15.5, value1.plus(value3).getValueExact());
+		assertEquals(52.076, value1.plus(value2).plus(value3).getValueExact(),
+				0.001);
 		
 		// make sure addition uses the correct unit, and is still associative
 		// (ignoring floating-point rounding errors)