Decimal places: Decimal places count digits after the decimal point.
Worked example
Round 6.4872 to 2 decimal places.
Step by step
- Look at the third decimal digit: 7.
- So round the second decimal digit up.
Final answer
6.49
Do not stop too early: You round based on the next digit after the last place you want to keep.
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Significant figures: Significant figures start from the first non-zero digit.
Worked example
Round 0.004786 to 2 significant figures.
Step by step
- The first two significant digits are 4 and 7.
- The next digit is 8, so round up.
Final answer
0.0048
| Value | 2 s.f. |
|---|---|
| 5381 | 5400 |
| 0.03812 | 0.038 |
| 91.46 | 91 |
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| Type | Example |
|---|---|
| Exact | 12 students |
| Approximate | length = 12.3 cm |
Measured values are usually approximate: Measurements are normally rounded, so they are rarely exact.
Quick classification
Which is exact: 25 people in a room, or a mass of 25 kg?
Step by step
- People are counted exactly.
- Mass is measured, so 25 kg is usually approximate.
Final answer
25 people is exact; 25 kg is approximate.
Follow the question: If the question says 3 significant figures, give 3 significant figures.
If it says nearest integer, do exactly that.
Worked example
A calculator gives 17.826492.
Write it to (a) 1 d.p.
(b) 3 s.f.
Step by step
- 1 d.p.
- 3 s.f.
Final answer
17.8 in both cases
Same answer, different reason: Sometimes different rounding instructions give the same final number, but you still need to understand why.