Tanya wants to estimate 61 + 68. She rounds both DOWN to 60 and adds: 60 + 60 = 120
Tanya wants to estimate 61 + 68. She rounds both DOWN to 60 and adds: 60 + 60 = 120. But the real answer is 129. Her friend says rounding each to the NEAREST ten gives a better estimate. Who is right?
Who do you think is right? Pick one.
The answer: Her friend is right, round to the nearest ten: 60 + 70 = 130, very close to 129
Why
Tanya rounded both numbers the same direction — both down — and each time she rounded down, she threw away a little bit of the real value: 61 lost 1, and 68 lost 8, so her estimate came out 9 short. The fix is to round each number to whichever ten is CLOSEST: 61 is nearest to 60, but 68 is nearest to 70, not 60. Then 60 + 70 = 130, and the small errors (down 1, up 2) mostly cancel instead of piling up. Test it: her way gives 120 (off by 9); rounding to the nearest ten gives 130 (off by just 1) — much closer to the true 129. Her friend is right: round each number to the nearest ten, not all the same direction — that keeps the errors from adding up.
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