To estimate, round every number to one significant figure and calculate with the rounded values. The result tells you roughly how big the true answer should be, and any answer that is far from it can be rejected at once.
This skill sits in non-calculator strategy and pairs naturally with keeping values exact. Estimating gives the size, exact working gives the value.
How do you estimate quickly?
- Round each number to one significant figure. 49.7 becomes 50, 6.1 becomes 6, and 812 becomes 800.
- Choose friendly numbers so the arithmetic is mental: 0.48 is close to 0.5, and 0.52 is close to 0.5.
- Calculate with the rounded numbers.
- Compare with your full answer, and ask whether it is the right size and, if the question allows, the right sign.
Worked example
Work out 49.7 × 6.1 and use an estimate to check the answer.
Step 1, estimate: 49.7 ≈ 50 and 6.1 ≈ 6. So 50 × 6 = 300.
Step 2, calculate in full: 49.7 × 6 = 298.2, and 49.7 × 0.1 = 4.97.
Step 3, add: 298.2 + 4.97 = 303.17.
Step 4, compare: 303.17 is close to 300, so the answer is plausible.
Now a second example with division.
Estimate 398 ÷ 0.52. Since 398 ≈ 400 and 0.52 ≈ 0.5, the estimate is 400 ÷ 0.5 = 800. The exact value is a little under 800.
So any answer near 80 or near 8000 is impossible.
The mistake to watch for
A common error is to multiply when the question needs division, then accept the result because the digits look plausible.
Mistaken working: 12 ÷ 0.4 = 4.8
The student multiplied 12 × 0.4 instead of dividing.
A one-line estimate shows the problem: 12 ÷ 0.5 = 24. Dividing by a number below 1 must give an answer bigger than 12, so 4.8 is impossible. The correct value is 12 ÷ 0.4 = 120 ÷ 4 = 30.
Check yourself
Try these without a calculator, then open each answer.
1. Estimate 7.9 × 4.1.
Show answer
7.9 ≈ 8 and 4.1 ≈ 4, so the estimate is 8 × 4 = 32. (The exact value is 32.39.)
2. A student says 298 ÷ 0.52 = 155. Use an estimate to decide whether this is possible.
Show answer
298 ≈ 300 and 0.52 ≈ 0.5, so the estimate is 300 ÷ 0.5 = 600. An answer of 155 is far too small, so it is impossible. Dividing by a number below 1 must make the answer bigger than 298.
3. A student finds 19.8% of 410 and writes 812. Explain why this must be wrong.
Show answer
19.8% is about 20%, and 20% of 400 is 80. So the answer should be about 80. An answer of 812 is bigger than the original 410, which is impossible for a percentage below 100%. (The exact value is 81.18.)
Where this leads next
Next, see how to keep long questions readable in organising working for a multi-operation task. For a mixed check of everything so far, try the non-calculator strategy practice set. The non-calculator working trainer and the percentage-base explorer both let you test your estimates against the exact results.
If estimating still feels like guesswork rather than a method, a teacher working through your own papers can show you where a two-second check would have saved marks. See online one-to-one Mathematics tuition.