Estimate to check calculations
Theory
To estimate a product or quotient, round each number to a friendly number, then multiply or divide — the answer is close but much quicker. Estimates are used to check whether an exact answer is reasonable.
To estimate a product or quotient, round each number to a friendly number, then multiply or divide the rounded numbers.
For a product, round each factor to its leading digit so only one non-zero digit is left.
An estimate is used to check an answer. If the exact answer is nowhere near the estimate, something has gone wrong.
Rounding up makes a number bigger; rounding down makes it smaller. This decides whether an estimate lands above or below the true answer.
| Calculation | Rounded | Estimate | Exact |
|---|---|---|---|
| \(39 \times 21\) | \(40 \times 20\) | \(800\) | \(819\) |
| \(43 \times 27\) | \(50 \times 30\) | \(1500\) | \(1161\) |
| \(592 \div 8\) | \(600 \div 8\) | \(75\) | \(74\) |
How to estimate to check a calculation
- Round each number to its leading digit, or for a division to a number the divisor goes into.
- Multiply or divide the rounded numbers in your head.
- Compare the estimate with the exact answer. If they are far apart, check the working.
| \(48 \times 31\) | \(\approx\) | \(50 \times 30\) |
| \(=\) | \(1500\) |
| \(592 \div 8\) | \(\approx\) | \(600 \div 8\) |
| \(=\) | \(75\) |
The estimate is \(50 \times 6 = 300\).
\(2820\) is about ten times too big, so the answer is not reasonable.
Both factors were rounded up.
So the estimate is an overestimate; the exact product is \(1161\).
Common pitfalls
Frequently asked questions
How do you estimate a multiplication?
Round each factor to its leading digit, then multiply the rounded numbers. \(48 \times 31\) is about \(50 \times 30 = 1500\).
How do you round the numbers in a division?
Round the first number to one the divisor goes into exactly. For \(592 \div 8\), use \(600 \div 8 = 75\), which is easy to do in your head.
How does an estimate check an answer?
Compare the estimate with the exact answer. If they are close, the answer is reasonable. If the answer is far from the estimate, the working needs checking.
What is an overestimate?
An estimate that is bigger than the true answer. Rounding both numbers up gives an overestimate; rounding both down gives an underestimate.
Why does a wrong answer often look ten times too big?
A misplaced zero or a lost column shifts every digit one place, making the answer about ten times too big or too small. The estimate makes this easy to spot.