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Estimate sums by rounding

Estimating sums by rounding involves rounding whole-number addends within 1,000 to the nearest ten or hundred, using the value of the digit to the right to decide whether to round up or down, and then adding the rounded numbers to obtain a reasonable approximate sum. The estimate preserves the magnitude of the exact sum and supports checking whether an answer is sensible; decimal numbers, larger-number algorithms, and formal error bounds are beyond this understanding.

Detailed Explanation: Estimate sums by rounding

To estimate a sum, round each addend first. Then add the rounded numbers.

  • To round to the nearest ten, look at the ones digit.
  • To round to the nearest hundred, look at the tens digit.
  • If the digit is 55 or more, round up. If it is less than 55, round down.

Example: Estimate 468+231468+231 by rounding to the nearest ten.

  1. Round 468468 to the nearest ten. The ones digit is 88, so round up:
468≈470468\approx470
  1. Round 231231 to the nearest ten. The ones digit is 11, so round down:
231≈230231\approx230
  1. Add the rounded numbers:
470+230=700470+230=700

So, the estimated sum is:

700\boxed{700}

The exact sum is 699699, so 700700 is a reasonable estimate.

Learn by doing: Estimate sums by rounding

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