Math & Science · Guide
Significant Figures: Rules, Examples and Practice
Five counting rules, two calculation rules, and a set of practice questions to lock them in.
Want the answer for your own numbers? Use the free Sig Fig Calculator — it does every step below for you.
The five counting rules
- Non-zero digits always count. 457 has 3.
- Zeros between non-zero digits count. 2.009 has 4.
- Leading zeros never count. 0.0069 has 2.
- Trailing zeros after a decimal point count. 0.06900 has 4; 12.50 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous. 100 could have 1, 2 or 3. Write 1.00 × 10² to show 3.
Worked examples
| Number | Sig figs | Reason |
|---|---|---|
| 0.06900 | 4 | 6, 9 and two trailing zeros after the decimal; leading zeros skipped |
| 100 | 1 (ambiguous) | No decimal point, so the zeros are placeholders |
| 100. | 3 | The decimal point makes the zeros significant |
| 1000 | 1 (ambiguous) | Write 1.000 × 10³ for 4 |
| 2.009 | 4 | Zeros sandwiched between digits count |
| 3.40 × 105 | 3 | Only the digits before × count |
Rounding to significant figures
Count from the first non-zero digit, then round the next digit as usual.
- 233.356 to two sig figs: the first two are 2 and 3; the next digit is 3, so round down. Answer: 230.
- 2.009 to two sig figs: 2.0 (the next digit, 0, rounds down).
- 0.006 849 to two sig figs: 0.0068.
- 45,678 to three sig figs: 45,700.
Adding and subtracting: count decimal places
Round the answer to the fewest decimal places in any number you added.
Express the sum to the right precision: 12.52 + 349.0 + 8.24
Raw sum: 369.76. The fewest decimal places is one (349.0).
369.8
Multiplying and dividing: count sig figs
Round the answer to the fewest significant figures in any input.
Example: 3.24 × 2.1
Raw product: 6.804. 2.1 has only two sig figs.
6.8
Exact numbers — counted items or defined values like 100 cm in a metre — have unlimited sig figs and never limit the answer.
Sig figs in scientific notation
Scientific notation removes the guesswork, because only the digits in front of “× 10” count. To convert, move the decimal point until one non-zero digit sits in front of it:
- 0.000560 = 5.60 × 10−4 — 3 sig figs (the trailing zero stays).
- 45,000 written as 4.5 × 104 has 2 sig figs; as 4.500 × 104 it has 4.
This is the cleanest way to show exactly how precise a whole number like 45,000 is.
Calculations with several steps
Keep extra digits during the working, and round only at the end. Rounding at every step can push the answer off.
Example: (12.5 + 3.27) × 2.0
Add first: 12.5 + 3.27 = 15.77. The sum is good to one decimal place (15.8), but carry 15.77 forward.
Multiply: 15.77 × 2.0 = 31.54. The product is limited to two sig figs by 2.0.
32
Sig figs vs decimal places
| Number | Sig figs | Decimal places |
|---|---|---|
| 12.50 | 4 | 2 |
| 0.0045 | 2 | 4 |
| 305.1 | 4 | 1 |
| 7.0 | 2 | 1 |
Decimal places count digits after the point. Sig figs count meaningful digits from the first non-zero one. Addition uses decimal places; multiplication uses sig figs.
Logarithms, for chemistry
When you take a log — for pH, for example — the number of decimal places in the answer equals the number of sig figs in the original number. log(2.50 × 103) = 3.398: three sig figs in, three decimal places out.
Practice questions
- How many sig figs in 0.00450?
- How many sig figs in 7,020?
- Round 0.0582749 to three sig figs.
- Round 98,451 to two sig figs.
- 15.2 + 3.456 + 0.71 = ?
- 4.56 × 0.0021 = ?
- How many sig figs in 6.020 × 1023?
- Divide 9.000 by 3.0.
Answers
- 3 (4, 5 and the trailing zero)
- 3 (the trailing zero is ambiguous; 7, 0 between and 2 count)
- 0.0583
- 98,000
- 19.4 (raw 19.366; fewest decimals is one)
- 0.0096 (raw 0.009576; two sig figs)
- 4
- 3.0 (two sig figs, from 3.0)
Print this section as a quick worksheet, and check any number in the sig fig calculator.
Frequently asked questions
230. The first two significant digits are 2 and 3, and the next digit is 3, so you round down and keep the zero as a placeholder.
Four. The leading zeros do not count, but the 6, the 9 and both trailing zeros after the decimal point do.
Add normally, then round to the fewest decimal places among the numbers you added. 12.52 + 349.0 + 8.24 = 369.76, which rounds to 369.8.
Only at the end. Keep at least one or two extra digits through each step, then round the final answer using the rule for the last operation. Rounding early builds up error.
It is ambiguous — at least 2. The trailing zeros may just be placeholders. Write 4.5 × 104 for 2 sig figs or 4.5000 × 104 for 5, so the reader knows which you mean.