Decimal places and significant figures
To round, find the last digit you keep, then look at the next one: 5 or more rounds up, less than 5 stays.
- 3.4682 to 2 decimal places: keep 3.46, next digit 8, so 3.47
- 48,652 to 2 significant figures: keep 48, next digit 6, so 49,000
- 0.004572 to 2 significant figures: the zeros at the start do not count, keep 45, next digit 7, so 0.0046
A rounded number keeps its size. 48,652 to 2 significant figures is 49,000, not 49.
Estimating
Round every number to 1 significant figure, then work it out.
- (38.7 × 5.13) ÷ 0.21
- ≈ (40 × 5) ÷ 0.2
- = 200 ÷ 0.2 = 1000
If every number was rounded up in a multiplication, the estimate is too big (an overestimate). Dividing by a number that was rounded down also makes the estimate bigger.
Truncating just cuts digits off: 3.79 truncated to 1 decimal place is 3.7, where rounding gives 3.8.
Use the calculator, then round
Work out √(7 × 2.4 + 53) ÷ 4.6 in one go, using brackets so the root covers the whole sum. Write down every digit the calculator shows, then round to 3 significant figures. Now leave the brackets out and see how far wrong it goes.