Estimate 73.6 × 88.4 within 1%

Question

Solve in your head. Estimate 73.6 	imes 88.4 to within 1\%. Aim: under 15 seconds.

Accepted Answer

Round the second factor up to a clean 90: 88.4 = 90 - 1.6, so 73.6 	imes 88.4 = 73.6 	imes 90 - 73.6 	imes 1.6. - 73.6 	imes 90 = 6624. - 73.6 	imes 1.6 = 117.76 \approx 118. 6624 - 118 \approx 6506. Exact answer: 6506.24, so the estimate is within 0.004\%. Rounding 88.4 	o 90 alone overshoots by about 1.8\%, which is why the -118 correction is essential; its own rounding (117.76 	o 118) is a sub-percent tail you can safely drop. Takeaway. You can round either factor, pick whichever gives the cleaner anchor (90 here). Round-up-and-subtract works exactly like round-down-and-add: one rou…

Estimate 73.6 × 88.4 within 1%

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