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Estimate sums

Estimation of sums involves using place-value understanding to round multi-digit whole-number addends to a specified place or choose compatible numbers, then combine the resulting values to produce a reasonable approximation. The estimate is interpreted as distinct from the exact sum and used to judge whether an exact calculation is sensible, with number lines helping show how rounding changes quantities; decimal and fraction sums and formal error bounds are not included.

Detailed Explanation: Estimate sums

To estimate a sum, round each addend to the place named in the problem, then add the rounded numbers. An estimate is close to the exact answer, but it is not the exact answer.

Example: Estimate 4,782+2,1694{,}782+2{,}169 to the nearest hundred.

  1. Round each number to the nearest hundred.
    • For 4,7824{,}782, look at the tens digit, 88. Since 88 is 55 or greater, round up:
4,782≈4,8004{,}782\approx4{,}800
  • For 2,1692{,}169, look at the tens digit, 66. Since 66 is 55 or greater, round up:
2,169≈2,2002{,}169\approx2{,}200

On a number line, 4,7824{,}782 is closer to 4,8004{,}800 than to 4,7004{,}700. Likewise, 2,1692{,}169 is closer to 2,2002{,}200 than to 2,1002{,}100.

  1. Add the rounded numbers.
4,800+2,200=7,0004{,}800+2{,}200=7{,}000
  1. State the estimate.
4,782+2,169≈7,0004{,}782+2{,}169\approx7{,}000

The estimated sum is 7,0007{,}000. The exact sum is 6,9516{,}951, so the estimate is reasonable and close, but it is not the exact answer.

Learn by doing: Estimate sums

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    Addition - Estimate Sum - 2 & 2 Digit

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