Estimate & check reasonableness by rounding
Theory
An estimate is a quick, rough answer found by rounding the numbers first. This Year 5 maths page shows how to round to the nearest ten, hundred or thousand, estimate sums and differences, choose a sensible level of rounding, and use an estimate to check whether an answer is reasonable.
To round a number, find the two round numbers it lies between and choose the closer one. \(2347\) is between \(2300\) and \(2400\) and is closer to \(2300\).
Look at the digit just to the right of the place you are rounding to: \(5\) or more rounds up, \(4\) or less rounds down. \(586\) rounds to \(600\) (nearest hundred) because the tens digit is \(8\).
An estimate uses the rounded numbers to get a quick answer. The symbol \(\approx\) means “is approximately equal to”.
An answer is reasonable if it is close to the estimate. If it is far away (for example ten times too big), there is probably a mistake.
Round first, then calculate:
How to estimate a sum or difference
- Choose a place to round to (ten, hundred or thousand).
- Round each number using the digit to the right.
- Add or subtract the rounded numbers.
How to check reasonableness
- Estimate the answer.
- Compare with the calculated answer.
- If they are far apart, check the working, especially lining up and carrying.
\(2347 \approx 2300\) and \(586 \approx 600\).
| \(2300 + 600\) | \(=\) | \(2900\) |
The estimate is \(2900\), which is close to the exact answer of \(2933\).
| \(670 + 250\) | \(=\) | \(920\) |
\(673 \approx 670\) and \(248 \approx 250\), so the estimate is \(920\).
| \(7300 - 3900\) | \(=\) | \(3400\) |
The estimate is \(3400\). The exact answer is \(3370\).
| \(600 + 300\) | \(=\) | \(900\) |
No. The estimate is about \(900\), so \(9021\) is about ten times too big. The answer is \(921\).
(i) Why is rounding to the nearest thousand a poor choice?
(ii) Estimate by rounding to the nearest ten.
| \(4390 + 70\) | \(=\) | \(4460\) |
(i) \(67\) would round to \(0\), so it is ignored completely.
(ii) \(4460\). The exact answer is \(4452\).
(i) Estimate the total to the nearest hundred.
(ii) Find the exact total.
(iii) By how much is the estimate out?
| \(5200 + 2900\) | \(=\) | \(8100\) |
| \(5150 + 2870\) | \(=\) | \(8020\) |
| \(8100 - 8020\) | \(=\) | \(80\) |
(i) \(\$8100\).
(ii) \(\$8020\).
(iii) The estimate is \(\$80\) too high (an overestimate).
| \(49\,000 + 31\,000\) | \(=\) | \(80\,000\) |
The estimate is \(80\,000\). The exact answer is \(80\,167\).
Common pitfalls
Frequently asked questions
How do you estimate by rounding?
Round each number to the same place, such as the nearest hundred, then add or subtract. \(2347 + 586 \approx 2300 + 600 = 2900\).
Why is estimating useful?
It tells you roughly what the answer should be, so mistakes such as a misplaced digit stand out.
How do you know if an answer is reasonable?
Compare it with your estimate. If \(642 + 279\) is estimated at \(900\), an answer of \(9021\) is not reasonable.
What does the symbol ≈ mean?
It means approximately equal to, for example \(673 + 248 \approx 920\).
Which place should I round to?
Round so that the numbers are easy to work with but none of them becomes zero. The nearest ten or hundred is usually best for three- and four-digit numbers.