Significant figures show up on every chemistry quiz, every physics lab report, and every standardized science exam — and most students learn the rules wrong the first time. If you have ever written down too many digits, dropped a zero you needed, or gotten marked off for rounding incorrectly, this guide is for you.

**TLDR: Significant Figures** walks you through everything that matters: what sig figs actually represent (measurement precision, not math pedantry), how to count them without getting tripped up by zeros, and why scientific notation is the cleanest way to eliminate all ambiguity. You will learn the standard rounding rules and the half-even rule that most teachers never mention but that shows up in AP and college courses. Then the guide covers the two arithmetic rules — the decimal-place rule for addition and subtraction, the sig-fig rule for multiplication and division — and shows exactly how to apply each one with worked examples. It closes by connecting all of this to real lab reports, engineering tolerances, and the practical situations where sig figs matter versus where you can set them aside.

This guide is concise and stripped to essentials — no filler, no padding, just the explanations and examples a high school or early college student needs to stop losing points on sig-fig questions. Parents helping a student and tutors prepping a session will find it equally useful.

If you need to count significant figures correctly starting today, grab this guide and get oriented fast.

• Identify the number of significant figures in any measured value, including tricky cases with zeros and scientific notation
• Apply the correct sig-fig rules for addition, subtraction, multiplication, and division
• Round results properly, including the half-even (banker's) convention
• Distinguish between precision and accuracy, and recognize when sig figs apply (measurements) versus when they don't (exact counts and defined constants)
• Use scientific notation to remove ambiguity about which digits are significant

1. 1. What Significant Figures Actually Mean
   Introduces sig figs as a way of encoding measurement precision, distinguishing them from pure math digits.
2. 2. Counting Sig Figs: The Rules and the Zeros Problem
   Walks through the rules for counting significant figures, with heavy focus on the ambiguous role of zeros.
3. 3. Scientific Notation as the Cleanup Tool
   Shows how scientific notation eliminates sig-fig ambiguity and makes counting trivial.
4. 4. Rounding Rules, Including the One Nobody Teaches You
   Covers standard rounding and the half-even (banker's) rule used in science and statistics.
5. 5. Arithmetic With Sig Figs: Two Different Rules
   Explains the decimal-place rule for addition/subtraction and the sig-fig rule for multiplication/division, with worked examples.
6. 6. Where Sig Figs Live in the Real World
   Connects sig figs to chemistry lab reports, physics problems, engineering tolerances, and when to ignore them.