Estimate 58.3 × 62.9 within 1%

Question

Solve in your head. Estimate 58.3 	imes 62.9 to within 1\%. Aim: under 15 seconds.

Accepted Answer

Round one factor to something clean and correct with a first-order term: 58.3 = 60 - 1.7, so 58.3 	imes 62.9 = 60 	imes 62.9 - 1.7 	imes 62.9. - 60 	imes 62.9 = 3774. - 1.7 	imes 62.9 \approx 1.7 	imes 63 = 107.1 (the dropped 1.7 	imes 0.1 = 0.17 is negligible). 3774 - 107.1 \approx 3667. Exact answer: 3667.07, so the estimate is within 0.002\%, deep inside the 1\% band. A crude bracket first, 60 	imes 63 = 3780, confirms the magnitude before you refine. Takeaway. For a 1\% band, round one factor and subtract only the first-order correction. Rounding 58.3 	o 60 alone is a +2.9\% move…

Estimate 58.3 × 62.9 within 1%

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