Rounding and estimating

To round, find the last digit you keep, then look at the next one: 5 or more rounds up, less than 5 stays.

1. 3.4682 to 2 decimal places: keep 3.46, next digit 8, so 3.47

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.

An estimate is a quick, rough answer.

To estimate, round every number to 1 significant figure, then work it out.

1. (38.7 × 5.13) ÷ 0.21

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.

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.

1. 70 is between 64 = 8² and 81 = 9²
2. so √70 is between 8 and 9

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.