Significant Figures Practice- Complete Guide

What Are Significant Figures?

Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. When you measure something, your measurement tool determines how many digits you can legitimately record. Sig figs tell you which digits matter.

For example, if you weigh something on a basic bathroom scale and it reads 150 pounds, that "150" has different precision than if a lab scale reads 150.00 pounds. The trailing zeros in 150.00 are significant—they tell you the measurement was precise to the hundredths place.

Chemists, physicists, and engineers care about sig figs because sloppy handling of precision leads to false accuracy. Reporting "6.02214076 × 10²³" when your measuring cup only gives you 2 significant figures is misleading.

Rules for Identifying Significant Figures

Non-Zero Digits Are Always Significant

Any digit from 1-9 counts as a significant figure.

Example: 427 has three significant figures (4, 2, and 7).

Zeros Between Non-Zero Digits Are Significant

Zeros that sit between two non-zero digits always count.

Example: 1005 has four significant figures. The zeros between 1 and 5 matter.

Leading Zeros Are Never Significant

Zeros at the beginning of a number only serve as placeholders and carry no significance.

Example: 0.0038 has two significant figures (3 and 8). The zeros are just showing you the decimal place.

Trailing Zeros—It Depends

Zeros at the end of a number are significant only if there's a decimal point somewhere.

• 1200 has two significant figures (no decimal shown)
• 1200. has four significant figures (the decimal is visible, even if it's ".0")
• 1200.0 has five significant figures

Scientific Notation Makes It Obvious

Scientific notation eliminates ambiguity. When you write 1.2 × 10³, you clearly have two significant figures. The power of 10 is just a placeholder for magnitude.

The Sig Fig Rules for Calculations

Multiplication and Division

Round your answer to match the number with the fewest significant figures.

Example: (4.56) × (1.4) = 6.384

4.56 has three sig figs. 1.4 has two sig figs. Your answer rounds to 6.4 (two sig figs).

Addition and Subtraction

Round your answer to match the least precise decimal place.

This one trips people up. You don't count sig figs here—you find the column (tenths, hundredths, etc.) that's furthest to the right with uncertainty, and you round to that column.

Example: 12.11 + 18.0 = 30.11

18.0 is precise only to the tenths place. Your answer rounds to 30.1.

Intermediate Steps

Keep one extra digit during calculations, then round only at the final answer. Rounding at each step compounds errors.

Getting Started: Practice Problems

Work through these. Answers below.

Identify the Number of Significant Figures

1. 3.0700
2. 0.0048
3. 500
4. 7.63 × 10⁵
5. 900.0

Calculate with Proper Sig Figs

1. (2.4) × (1.67)
2. 15.2 + 7.93
3. (8.95) / (4.1)
4. 12.0 − 3.45

Answers:

1. 5 sig figs
2. 2 sig figs
3. 1 sig fig (or ambiguous—use scientific notation if you mean more)
4. 3 sig figs
5. 4 sig figs

1. 4.0
2. 23.1
3. 2.2
4. 8.6

Sig Fig Tools Compared

Sometimes you need help. Here's what works:

A calculator is fine for checking, but don't rely on it during exams unless explicitly allowed. You need to know the rules cold.

Common Mistakes to Avoid

• Forgetting the decimal point rule—trailing zeros only count with a decimal
• Applying multiplication rules to addition—they use different rounding criteria
• Rounding too early—keep extra digits through calculations
• Ignoring exact numbers—counted items (like "3 apples") are infinitely precise

Why This Matters

Sig figs aren't busywork. They're how scientists communicate uncertainty honestly. A calculation with excessive precision looks impressive but means nothing if your inputs were imprecise.

When you report 6.00 grams instead of 6 grams, you're saying "I measured this precisely." Sig figs tell your reader what your measurement actually says, not what you wish it said.