Estimation and Approximation Under Time Pressure
Approximate to decide
Estimation is a decision tool. Round each number to one or two significant figures, use compatible numbers that divide neatly, and keep track of order of magnitude. Benchmarks help: 10% is a decimal shift, 1% is a further shift, 5% is half of 10%, and 0.5 is a half. For products and quotients, rounding one number up and another down tends to keep the estimate balanced. Front-end estimation (add the leading digits first) gives a fast lower bound; rounding to nearest gives a central estimate. In data questions, estimate the answer before reading the options, then choose the closest.
Traps
Rounding too early or too aggressively can move the answer outside a narrow option set. Rounding every number in the same direction biases the result. Percentage errors of scale are common: 0.5% is not 5%, and 1.5 million is 1,500,000, not 150,000. Do not confuse a 10% increase with a tenfold increase. Keep units attached throughout; an estimate of “about 1,700” is meaningless without knowing whether it is pounds, thousands of pounds or units.
Worked example
Estimate 4,187 × 0.198 ÷ 0.51. Use 4,200 × 0.2 ÷ 0.5 = 840 ÷ 0.5 = 1,680. The exact value is about 1,626, so the estimate is within 4% and would identify the correct option among 162, 1,626 and 16,260.
Rule of thumb: estimate first to eliminate options, then calculate only to separate the final two.