Reference library69 entries

Author: Tommy C. Moran

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

Significant Figures

Are Leading Zeros Significant? (No — Here’s Why)

Leading zeros are never significant. They are placeholders that indicate the position of the decimal point. This article explains the rule, its rationale, and…

Read explanation

Significant Figures

How Many Significant Figures Does 0.00456 Have?

Learn exactly why 0.00456 has three significant figures, with clear rules, worked examples, common pitfalls, and references to NIST, ISO, and ASTM standards. This…

Read explanation

Counted Numbers vs Measured Numbers: Precision and Significant Figures

Counted numbers are exact and have infinite significant figures, while measured numbers carry uncertainty and are limited by the instrument's precision. This guide explains…

Read explanation

Rounding Methods

Why Different Calculators Give Different Rounded Answers

Different calculators produce different rounded results due to variations in rounding conventions, internal floating-point precision, and display settings. This guide explains the underlying causes,…

Read explanation

Why Python’s round() Uses Banker’s Rounding: A Precision Reference

Python's round() implements banker's rounding (round half to even) to reduce cumulative bias in statistical operations. This article explains the rationale, standards, and practical…

Read explanation

Significant Figures

Significant Figures of Zero Itself: Rules, Conventions, and Pitfalls

Zero is the most ambiguous digit in significant figures. Learn the rules for leading, trailing, and captive zeros, plus conventions and standards.

Read explanation

Significant Figures

Do Constants Like π and c Affect Significant Figures?

Constants such as π, e, and c are exact or have defined values, so they do not limit the number of significant figures in…

Read explanation

Addition and Subtraction

Why Addition and Multiplication Use Different Sig Fig Rules

Addition and multiplication follow different significant figure rules because they propagate uncertainty differently: addition uses absolute uncertainty, multiplication uses relative uncertainty.

Read explanation

Significant Figures

Are Trailing Zeros Significant? It Depends on the Decimal Point

Trailing zeros are significant only when a decimal point is present. Without a decimal point, they are ambiguous and require scientific notation or an…

Read explanation

Significant Figures in Engineering Drawings and Tolerances

{ “title”: “Significant Figures in Engineering Drawings and Tolerances: Precision Standards and Best Practices”, “slug”: “significant-figures-engineering-drawings-tolerances”, “excerpt”: “Learn how significant figures govern engineering drawings…

Read explanation