Estimating is used to quickly obtain an approximate answer to a calculation.

Round each number in the calculation to 1 significant figure, then perform the calculation.

For example, estimate 379 x 415:

379, to 1 significant figure, is 400;

415, to 1 significant figure, is also 400;

400 x 400 = 160 000.

Compare the estimated answer 160 000 with the actual answer 379 x 415 = 157 285. Note that the number of digits in each answer is the same, and that the answers are reasonably close to each other.

For numbers that are a single digit: e.g. 8, do not round the digit.

Sometimes it is easier to identify simpler calculations: frac(1800)(6) is simpler to treat as 1800 ÷ 6, rather than round 1800 to 2000 and then to divide 2000 by 6.

Note that the sign means approximate: the value on one side of this sign is approximately equal to the value on the other side of the sign.

## Example 1

Holly is buying some clothes in a shop. She is buying four items at £3.56, £42.49, £18.99 and £0.99. Estimate how much she is spending.

Rounding to one significant figure: 4 + 40 + 20 + 1 = 65.

The accurate answer is £66.03.

Note that as the question asked for an estimate, an answer of £66.03 would be marked as wrong.

## Example 2

Adam has ended up with the following calculation: frac(205 times 89)(3244) Estimate the answer he should expect.

frac(205 times 89)(3244)frac(200 times 90)(3000)

= frac(18000)(3000)

= frac(18)(3)

= 6

The accurate answer is 5.624 (3dp).