Estimate & check reasonableness by rounding
Theory
To estimate, round each number to a nearby friendly number, then calculate — the answer is close but much quicker. Estimates are used to check whether an exact answer is reasonable.
To estimate, round each number to a nearby friendly number — the nearest ten, hundred or thousand — then add or subtract.
A digit of \(5\) or more rounds up; less than \(5\) rounds down.
An estimate is used to check an answer. If the exact answer is nowhere near the estimate, something has gone wrong.
Round each number to a friendly place, then calculate. A digit of \(5\) or more rounds up.
| Number | Nearest ten | Nearest hundred |
|---|---|---|
| \(487\) | \(490\) | \(500\) |
| \(312\) | \(310\) | \(300\) |
| \(1438\) | \(1440\) | \(1400\) |
How to estimate a calculation
- Round each number to the nearest ten, hundred or thousand.
- Add or subtract the rounded numbers.
- Compare the estimate with the exact answer to check it is reasonable.
| \(1438 + 129\) | \(\approx\) | \(1440 + 130\) |
| \(=\) | \(1570\) |
| \(487 + 312\) | \(\approx\) | \(500 + 300\) |
| \(=\) | \(800\) |
The estimate is about \(800\).
\(7990\) is far too big, so the answer is not reasonable.
| \(612 - 288\) | \(\approx\) | \(600 - 300\) |
| \(=\) | \(300\) |
Common pitfalls
Frequently asked questions
How do you estimate a calculation?
Round each number to a friendly place, then add or subtract. \(487 + 312\) is about \(500 + 300 = 800\).
Why do we round before adding?
Rounded numbers are quick to add in your head, giving an answer close enough to check the exact one.
How do you check if an answer is reasonable?
Compare it with an estimate. If the answer is far from the estimate, it is probably wrong and the working needs checking.
When does a number round up?
When the digit in the place you are looking at is \(5\) or more. Less than \(5\) rounds down. So \(487\) rounds up to \(500\).