Approximation and Estimation
What you must understand
Some questions ask for an approximate answer or expect you to choose between close options quickly. The skill is rounding numbers to convenient values so the arithmetic becomes mental, while keeping the error small enough to identify the correct option.
Method
Round each number to one or two significant figures, perform the simplified calculation, then check whether the options are far enough apart to make the estimate decisive. For division, round numerator and denominator in the same direction where possible so errors partly cancel. For percentages, round to friendly fractions: 24% ≈ 25% = one quarter; 33% ≈ one third; 48% ≈ one half.
Traps
- Rounding both numbers in a way that compounds error in the same direction.
- Rounding before deciding whether the question needs an exact answer.
- Losing a factor of ten when rounding 0.49 to 0.5.
- Options placed close together, where an estimate cannot discriminate; then compute exactly.
- Forgetting that an estimate should be checked against the order of magnitude.
Worked example
Estimate 4,912 × 0.198. Round to 5,000 × 0.2 = 1,000. The exact value is about 973, so the estimate is within 3% - sufficient to pick 973 from options such as 97, 973, 9,730 and 97,300. The order of magnitude rules out three of them immediately.