Reference library25 entries

Tag: GUM

Practical explanations, worked examples, and reference notes for reporting numbers correctly.

Truncation vs Rounding: When Cutting Digits Is Correct

Truncation and rounding are distinct digit-reduction methods. Truncation simply cuts off excess digits, while rounding adjusts the retained digits based on the discarded portion.…

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Exact Numbers Have Infinite Significant Figures — Here’s What That Means

Exact numbers, such as counted quantities and defined conversion factors, possess an infinite number of significant figures. This article explains the rule, provides worked…

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Error Propagation

Propagating Uncertainty Through Addition and Multiplication: Rules, Examples, and Standards

Learn how to propagate uncertainty when adding, subtracting, multiplying, and dividing measured values. Understand the significant figure rules, the GUM approach, and common pitfalls.

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Double Rounding Error

The Double Rounding Error That Changes Your Final Answer

Double rounding—rounding an intermediate value and then rounding again—can produce a different final result than a single direct rounding. Learn the rules, standards, and…

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Ambiguous Trailing Zeros

The Overline (Bar) Notation for Ambiguous Trailing Zeros

Learn how the overline (bar) notation resolves ambiguity in trailing zeros, with rules, examples, standards citations, and common pitfalls.

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How Unit Conversion Factors Affect Significant Figures

Learn how unit conversion factors influence the number of significant figures in your results. Understand exact vs. inexact conversions, rounding rules, and standards.

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Rounding Methods

Round Half Up vs Round Half Even: Which Does Your Class Use?

A comprehensive comparison of two common tie-breaking rules for rounding, including definitions, examples, standards, and software behavior.

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Rounding vs Significant Figures

Rounding vs Significant Figures: Not the Same Thing

Rounding and significant figures are often confused, but they serve different purposes. Rounding reduces digits; significant figures convey precision. Learn the rules, standards, and…

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Scientific Notation

How to Convert Any Number to Scientific Notation: Rules, Examples, and Pitfalls

A comprehensive guide to converting numbers to scientific notation, covering rules, conventions, standards, and common mistakes, with worked examples and practice problems.

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Significant Figures in Logarithms and pH: The Definitive Guide

Learn the precise rules for determining significant figures in logarithms and pH values, with worked examples, common pitfalls, and standards citations.

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