Rounding and estimating
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
The significant figures of a number start at its first digit that is not zero. In 48,652 the first significant figure is 4; in 0.004572 it is 4 as well.
- Rounding to 2 decimal places (d.p.) keeps 2 digits after the point.
- Rounding to 2 significant figures (s.f.) keeps 2 digits from the first significant one.
A rounded number keeps its size. 48,652 to 2 significant figures is 49,000, not 49: fill the places after the kept digits with zeros.
When rounding up carries over, keep the zeros that show the accuracy: 29.96 to 1 decimal place is 30.0 (keep 29.9, next digit 6, round up), and the 0 after the point is written.
Estimating
An estimate is a quick, rough answer.
To estimate, 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.
Calculators and square roots
On a calculator, put brackets round the whole top and the whole bottom of a fraction, and round the whole sum under a root sign, then round only the final answer.
(2 + 3.5²) ÷ (√50 − 1) needs both pairs of brackets.
A square root lies between the square roots of the square numbers either side of it.
- 70 is between 64 = 8² and 81 = 9²
- so √70 is between 8 and 9
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.
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