Decimal places (d.p.) count digits after the decimal point. Significant figures (s.f.) count all meaningful digits from the first non-zero digit. Both are ways of rounding a number to a given level of precision — the rounding rule is the same: look at the next digit and round up if it is 5 or more.
What are decimal places?
Decimal places count how many digits appear after the decimal point. The number 3.14159 rounded to 2 d.p. is 3.14, because you keep two digits after the point and check the third (1 < 5, so round down, keeping 3.14).
| Number | 1 d.p. | 2 d.p. | 3 d.p. |
|---|---|---|---|
| 7.3862 | 7.4 | 7.39 | 7.386 |
| 0.0574 | 0.1 | 0.06 | 0.057 |
| 12.995 | 13.0 | 13.00 | 12.995 |
Note that 12.995 rounded to 2 d.p. is 13.00, not 13 — the trailing zeros after a decimal point show the precision you used.
What are significant figures?
A significant figure is any digit that carries meaning about the size of the number. The rules for identifying significant figures are:
- The first significant figure is the first non-zero digit.
- Every digit after the first significant figure counts — including zeros between digits and trailing zeros after the decimal point.
- Leading zeros (zeros before the first non-zero digit) do not count.
Examples:
- 3 s.f.: 4730 → first sig. fig. is 4; second is 7; third is 3.
- 3 s.f.: 0.00605 → first sig. fig. is 6; second is 0; third is 5.
How do you round to a given number of significant figures?
Step-by-step method:
- Identify the digit in the position you want (e.g. the 2nd significant figure).
- Look at the next digit to the right.
- If it is 5 or more, round the identified digit up by 1. If it is 4 or less, leave it unchanged.
- Replace all digits to the right of your rounding position with zeros (for whole numbers) or drop them (for decimals).
Worked example 1 — round 47 382 to 3 s.f.:
- First s.f. = 4 (ten-thousands), second = 7 (thousands), third = 3 (hundreds). That is the digit we keep.
- Next digit = 8 (tens). Since 8 ≥ 5, round 3 up to 4.
- Replace everything after the hundreds place with zeros: 47 400.
Worked example 2 — round 0.006 284 to 2 s.f.:
- First s.f. = 6, second s.f. = 2. Keep up to the 2.
- Next digit = 8. Since 8 ≥ 5, round 2 up to 3.
- Answer: 0.0063.
What is the key difference between d.p. and s.f.?
| Feature | Decimal places | Significant figures |
|---|---|---|
| What is counted | Digits after the decimal point | All meaningful digits from the first non-zero |
| Useful for | Numbers near 1 (e.g. measurements) | Very large or very small numbers |
| Example: 0.00456 to 2 | 0.00 (two d.p.) | 0.0046 (two s.f.) |
| Example: 72 300 to 3 | Not meaningful (no decimal) | 72 300 (three s.f.) |
How do you handle zeros when rounding to significant figures?
Zeros can be tricky:
- 0.00503 to 2 s.f.: first s.f. = 5, second s.f. = 0, next digit = 3 (< 5, round down). Answer: 0.0050. The trailing zero after the 5 is significant here.
- 8 040 to 2 s.f.: first s.f. = 8, second s.f. = 0, next digit = 4 (< 5, round down). Answer: 8 000. The zeros here are placeholders, not significant.
Worked example: applying both methods to the same number
Round 5.3748 to:
- 2 decimal places: Look at the 3rd digit after the point (4). Since 4 < 5, round down. Answer: 5.37.
- 2 significant figures: First s.f. = 5, second s.f. = 3. Next digit = 7. Since 7 ≥ 5, round 3 up to 4. Answer: 5.4.
Notice the two methods give different answers — they are measuring precision in different ways.
Frequently asked questions
Why do leading zeros not count as significant figures?
Leading zeros (like the zeros in 0.0047) simply tell you the size of the number — they are place-holders that locate the decimal point. They carry no independent information about precision. The first meaningful digit in 0.0047 is 4, so that is the first significant figure.
What happens when rounding up causes a carry?
If rounding up changes a 9 to a 10, carry over to the next column. For example, 0.00596 to 2 s.f.: first s.f. = 5, second s.f. = 9. Next digit = 6 ≥ 5, so round 9 up to 10, carry 1 to the 5, giving 0.0060. Write the trailing zero to show 2 s.f. have been used.
Should I write trailing zeros after the decimal point?
Yes, when the question asks for a specific number of decimal places or significant figures. Writing 3.70 (2 d.p.) tells the reader that you rounded to the nearest hundredth; writing 3.7 implies only 1 d.p. of precision. In exams, omitting trailing zeros can lose accuracy marks.
When would a scientist use significant figures rather than decimal places?
Scientists use significant figures when working with quantities that span very different scales — for instance, atomic radii (0.000 000 000 1 m) and distances between galaxies (9.5 × 10²⁰ m). Significant figures keep precision consistent regardless of the magnitude of the number, which is why they appear alongside standard form at GCSE Science as well as Maths.
For Socratic number and rounding practice, see aitutors.me.