Significant Figures Practice- Free Worksheet
What Are Significant Figures?
Significant figures (also called sig figs) are the digits in a number that carry meaningful information about its precision. When you measure something, your measurement only reflects the precision of your measuring tool. Sig figs tell you exactly how precise that measurement is.
For example, if you weigh something on a basic bathroom scale and it shows 150 pounds, you know it's between 149.5 and 150.5. But if you use a lab scale and it shows 150.00 pounds, that "00" tells you the measurement is precise to the hundredths place. The zeros in 150.00 are significant—they're not just placeholders.
The Rules for Identifying Significant Figures
Here's how to count them, step by step:
Rule 1: Non-zero digits are always significant
In 347, all three digits are significant. In 8.29, all three are significant. This one's straightforward.
Rule 2: Zeros between non-zero digits are significant
The zero in 101, 405, and 1.03 counts. You're not guessing whether that zero is there—it actually represents a measured value.
Rule 3: Leading zeros are never significant
The zeros at the start of 0.0056 or 0.042 are just placeholders showing you the location of the decimal point. They don't add precision. 0.0056 has only two significant figures: 5 and 6.
Rule 4: Trailing zeros are significant only if there's a decimal point
This trips up most students. In 1,200, the trailing zeros are ambiguous. Without a decimal, we don't know if the measurement was precise to the tens place or exact. But 1,200. (with a decimal) or 1.200 × 10³ has four significant figures.
Rule 5: Exact numbers have infinite significant figures
If you count 3 apples, that "3" is exact. Conversion factors like 1 inch = 2.54 cm are defined values with unlimited sig figs. They don't limit your final answer's precision.
Quick Reference Table
| Number | Significant Figures | Why? |
|---|---|---|
| 7.53 | 3 | All non-zero digits count |
| 0.0082 | 2 | Leading zeros don't count |
| 4.00 | 3 | Trailing zeros after decimal count |
| 3,600 | 2 | No decimal shown—ambiguous |
| 3,600.0 | 5 | Trailing zero after decimal counts |
| 805 | 3 | Zero between non-zeros counts |
Calculations With Significant Figures
Addition and Subtraction
For addition and subtraction, look at the decimal places, not the number of sig figs. Your answer can only be as precise as your least precise measurement.
Example:
12.11 + 3.0 + 0.225 = ?
The least precise value is 3.0 (to the tenths place), so your answer rounds to 15.3. You can't claim more decimal places than your worst input allows.
Multiplication and Division
For multiplication and division, count the significant figures in each factor. Your answer gets the same number of sig figs as the factor with the fewest.
Example:
4.56 × 1.4 = ?
4.56 has three sig figs. 1.4 has two sig figs. Answer rounds to 6.4 (two sig figs).
Common Mistakes to Avoid
- Over-counting zeros — If a number looks like 1,000, assume nothing. Check if a decimal is written.
- Forgetting to round — Your calculator gives you 8.3472, but if you need 2 sig figs, that answer is 8.3.
- Mixing up addition/subtraction rules with multiplication/division rules — Decimal places for adding. Sig figs for multiplying.
- Dropping trailing zeros — Writing 6.0 as 6 loses information about precision.
Free Significant Figures Practice Worksheet
Work through these problems. Answers are at the bottom.
Part 1: Count the Significant Figures
- 3.407
- 0.0092
- 5,280
- 12.00
- 0.0550
- 7.654 × 10²
- 100.
- 0.0205
Part 2: Round to the Indicated Significant Figures
- 14.786 rounded to 3 sig figs
- 0.02753 rounded to 2 sig figs
- 1,299,432 rounded to 4 sig figs
- 8.95 rounded to 2 sig figs
Part 3: Solve and Report the Answer With Correct Sig Figs
- 23.4 + 8.72 + 6.1
- 115.0 − 47.32
- 6.48 × 3.8
- 84.6 ÷ 2.4
- (4.32 × 1.2) + 7.9
Answers
| Part 1 | Part 2 | Part 3 |
|---|---|---|
| 1. 4 | 1. 14.8 | 1. 38.2 |
| 2. 2 | 2. 0.028 | 2. 67.7 |
| 3. 3 (ambiguous—assume 2 without decimal) | 3. 1,299,000 | 3. 25 |
| 4. 4 | 4. 9.0 | 4. 35 |
| 5. 3 | — | 5. 13.1 |
| 6. 4 | — | — |
| 7. 3 | — | — |
| 8. 3 | — | — |
Getting Started: How to Check Your Work
Here's a simple process for any sig figs problem:
- Identify the number with the fewest sig figs (multiplication/division) or fewest decimal places (addition/subtraction).
- Calculate your answer using full precision on a calculator.
- Round your final answer to match the limiting factor.
- Check that trailing zeros in your answer are actually significant—if needed, use scientific notation.
This method works every time. No guessing required.
Why This Matters
Significant figures aren't busywork. They're the language of precision in science and engineering. Mess them up, and your "correct" answer is actually wrong in a lab report or on an exam. The rules exist because measurements have limits, and your reported values should reflect those limits honestly.
Print the worksheet above, work through every problem, and check your answers. That's it. Sig figs click faster when you actually practice them instead of just reading about them.