Estimate by rounding each number to a friendly value, calculate in your head, and compare with the calculator. If the two are far apart, find the error before you write the answer down.
The routine
- Round each number to one or two friendly figures.
- Do the quick calculation mentally.
- Work out the exact answer.
- Compare the size, the sign and the units.
An estimate takes only a few seconds, and it works on any numerical question in any subject.
Three worked examples
For 4.87 × 19.6, round to 5 × 20 = 100. The exact value is 95.452, which is close to 100, so it passes.
For 398 ÷ 7.9, round to 400 ÷ 8 = 50. The exact value is about 50.4, so it passes.
For 0.52 × 0.48, round to 0.5 × 0.5 = 0.25. The exact value is 0.2496, which matches.
A slip that estimation catches
A student calculates 6.1 × 29.7 and the screen shows 1811.7. The estimate is 6 × 30 = 180. The calculator answer is ten times too large, which suggests a decimal was entered wrongly, such as 297 instead of 29.7.
Retyping gives 181.17, which agrees with the estimate. Without the check, 1811.7 would have gone into the next line of the working.
Checking sign and sense
Estimation also checks direction. If you add a positive amount and the result gets smaller, something is wrong.
Ask these questions about any answer:
- Is the sign what I expect from the situation?
- Is the size realistic, for instance a length of 4 000 m for a classroom?
- Does the unit match what the question asked for?
The last point connects to checking units, signs, labels and task coverage.
Try it yourself
A student works out 3.96 × 51.2 and writes 20.27. Use an estimate to decide whether it is reasonable, then give the correct value.
Answer
Round to 4 × 50 = 200. The answer 20.27 is ten times too small, so the decimal point is misplaced.
The exact value is 3.96 × 51.2 = 202.752, which agrees with the estimate of 200. The digits were probably right and only the decimal position was wrong, which is why estimating the size first is worth the few seconds.
Next steps
Estimation pairs well with using brackets and operation order, because a wrong order of operations can give an answer of the wrong size. The signed numbers hub lists the other skills, and SPM Mathematics tuition offers one-to-one practice.