Estimate 68.7 × 41.3 within 1%

Question

Solve in your head. Estimate 68.7 	imes 41.3 to within 1\%. Aim: under 15 seconds.

Accepted Answer

Round one factor to something round and correct: 68.7 	imes 41.3 = 70 	imes 41.3 - 1.3 	imes 41.3. - 70 	imes 41.3 = 2891. - 1.3 	imes 41.3 \approx 1.3 	imes 41 = 53.3 (the neglected 1.3 	imes 0.3 is only 0.39). 2891 - 53.7 \approx 2837. Exact answer: 2837.31, the estimate is within 0.02\%, far inside the 1% band. A cruder check first: 70 	imes 41 = 2870, so anything near 2850 \pm 40 is plausible. Bracketing before refining catches sign and magnitude slips. Takeaway. For a 1% band you only need the two largest terms of the expansion, round one factor, multiply exactly, subtract the fi…

Estimate 68.7 × 41.3 within 1%

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