Estimate 47.8 × 53.2 within 1%

Question

Solve in your head. Estimate 47.8 	imes 53.2 to within 1\%. Aim: under 15 seconds.

Accepted Answer

Round the closer factor: 47.8 = 48 - 0.2, so 47.8 	imes 53.2 = 48 	imes 53.2 - 0.2 	imes 53.2. - 48 	imes 53.2 = 2553.6 (that is 48 	imes 53 = 2544, plus 48 	imes 0.2 = 9.6). - 0.2 	imes 53.2 = 10.64. 2553.6 - 10.64 \approx 2543. Exact answer: 2542.96, so the estimate is within 0.002\%. A crude bracket, 48 	imes 53 = 2544, already lands within a hair, the correction just polishes it. Takeaway. Anchor to the nearest round factor and subtract one first-order term. When both factors are close to round numbers, the crude product (48 	imes 53) is often already inside 1\%, and the correcti…

Estimate 47.8 × 53.2 within 1%

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