Estimate to check calculations
Theory
An estimate is a quick, rough answer found by rounding. It tells you what size the real answer should be, so you can catch mistakes. This Year 6 maths page shows how to estimate multiplications and divisions and how to tell whether an estimate is too big or too small.
Leading-digit rounding: round each number to its first digit followed by zeros. \(58 \to 60\), \(393 \to 400\).
For division, round to a friendly number that divides exactly: \(715 \div 9 \approx 720 \div 9 = 80\).
If every number was rounded up, the estimate is an overestimate; if every number was rounded down, it is an underestimate.
Compare the exact answer with the estimate. If it is about ten times too big or too small, a zero or decimal point is probably in the wrong place.
Estimating:
Estimating to check
- Round each number to its leading digit (or a friendly number for division).
- Calculate with the rounded numbers.
- Compare with the exact answer: it should be fairly close.
- Decide over or under from the directions of rounding.
| \(60 \times 30\) | \(=\) | \(1800\) |
About \(1800\). (Exact: \(1856\).)
| \(400 \times 6\) | \(=\) | \(2400\) |
About \(2400\). (Exact: \(2358\).)
| \(720 \div 9\) | \(=\) | \(80\) |
About \(80\).
(i) Is that an over- or underestimate?
(ii) The exact answer is \(5896\). How far out is it?
| \(6300 - 5896\) | \(=\) | \(404\) |
(i) Overestimate: both numbers were rounded up
(ii) \(404\)
| \(50 \times 50\) | \(=\) | \(2500\) |
One rounded down and one up, so the estimate is close: the exact answer is \(2491\).
| \(40 \times 7\) | \(=\) | \(280\) |
The answer should be about \(280\). \(2660\) has one zero too many; the answer is \(266\).
| \(5 \times 6\) | \(=\) | \(30\) |
About \(30\), so \(297.6\) is ten times too big. The answer is \(29.76\).
Common pitfalls
Frequently asked questions
What is an estimate?
A quick approximate answer found by rounding.
How do I round to the leading digit?
Keep the first digit (rounded) and replace the rest with zeros: \(58 \to 60\).
When is an estimate an overestimate?
When the numbers were rounded up.
How does an estimate check an answer?
If the answer is very different from the estimate, there is probably a mistake.
How do I estimate a division?
Round to a number that divides easily: \(715 \div 9 \approx 720 \div 9 = 80\).