Estimate 39.6 × 71.4 within 1%

Question

Solve in your head. Estimate 39.6 	imes 71.4 to within 1\%. Aim: under 15 seconds.

Accepted Answer

Round the factor nearest a round number: 39.6 = 40 - 0.4, so 39.6 	imes 71.4 = 40 	imes 71.4 - 0.4 	imes 71.4. - 40 	imes 71.4 = 2856. - 0.4 	imes 71.4 = 28.56 \approx 28.6. 2856 - 28.6 \approx 2827. Exact answer: 2827.44, so the estimate is within 0.02\%. Because 39.6 is only 1\% below 40, the correction term is small and easy, this is the friendliest case of the round-and-correct method. Takeaway. Round the factor that is closest to a round number: the nearer it is, the smaller the first-order correction. Here 0.4 	imes 71.4 \approx 28.6 is a trivial subtraction, and one term of the e…

Estimate 39.6 × 71.4 within 1%

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