Maths
What is estimation in maths?
Quick answer
Estimating means making a sensible guess at an answer, usually by rounding the numbers first. It tells you roughly what to expect and helps you spot mistakes.
In one sentence
Estimating is working out a close-enough answer quickly, without needing it to be exact.
Explained
Suppose you buy three things costing £2.95, £4.10 and £1.99. Before the till beeps, you can think: "about £3 + £4 + £2, so roughly £9." That is an estimate. The exact total is £9.04, very close.
basket
banana- banana
- banana
The usual way to estimate a calculation is to round the numbers to something easy, then calculate with those.
- 387 + 214 is about 400 + 200 = 600 (exact: 601)
- 52 × 7 is about 50 × 7 = 350 (exact: 364)
- 612 ÷ 3 is about 600 ÷ 3 = 200 (exact: 204)
Estimating is most useful as a check. Work out the exact answer, then compare it with your estimate. If you get 3,640 for 52 × 7, the estimate of 350 shouts that something has gone wrong (here, an extra zero).
There is a second kind of estimating: guessing a quantity you can see. How many sweets are in a jar? How long is the playground? A good trick is to use a benchmark. Count the sweets in one small section and multiply by the number of sections. Or remember that a big adult stride is about a metre, then pace the playground out. See length and measuring for more benchmarks.
An estimate is not a wild guess. It is a reasoned answer, and it should come with a reason.
Examples
| Question | Estimate | Exact |
|---|---|---|
| 28 + 63 | 30 + 60 = 90 | 91 |
| 405 − 198 | 400 − 200 = 200 | 207 |
| 19 × 21 | 20 × 20 = 400 | 399 |
| 4.9 × 6.1 | 5 × 6 = 30 | 29.89 |
| 1,189 ÷ 4 | 1,200 ÷ 4 = 300 | 297.25 |
Common mistakes
- Doing the exact calculation and calling it an estimate. Fix: round first, then calculate with the easy numbers.
- Rounding so roughly that the estimate is useless. For 1,450 + 1,480, rounding to the nearest thousand gives 2,000, but the real answer is 2,930. Rounding to the nearest hundred works better.
- Never checking. Make "does my answer match my estimate?" the last step of every calculation.
Quick quiz
Estimation
Check what you know with 4 quick questions.
Question 1 of 4
Which is the best estimate for 49 + 32?
Practise it
Try it
Mental maths and estimation practice
For grown-ups
Related topics
Rounding
Rounding means replacing a number with a simpler one that is close to it, such as 47 rounded to the nearest ten being 50. It makes numbers easier to work with.
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Length and measuring
Length is how long, tall or far something is. It is measured with a ruler or tape in units such as millimetres, centimetres, metres and kilometres (or inches, feet and miles).
Counting
Counting means saying one number for each thing in a group, in order, to find out how many there are. The last number you say is the total.
Mass and weight
Mass is how much stuff is in an object, measured in grams and kilograms. Weight is the pull of gravity on that mass. In everyday life people say weight for both.
Square roots
The square root of a number is the value that, multiplied by itself, gives that number. The square root of 25 is 5, because 5 × 5 = 25. The sign is √.