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Estimate differences

Estimating a difference involves using place-value understanding to round multi-digit whole numbers or terminating decimals, or to select compatible numbers, before subtracting to determine a reasonable approximate result. The estimate reveals the difference’s scale and supports checking whether an exact calculation is sensible; rounding must preserve the relevant relationship between the numbers, especially when they are close. This scope excludes signed numbers, fraction differences, and formal error bounds.

Detailed Explanation: Estimate differences

To estimate a difference, round the numbers first, then subtract the rounded numbers.

Example: Estimate 4,782−2,1464{,}782-2{,}146.

  1. Choose a place to round.
    Round to the nearest hundred because both numbers have hundreds places.

  2. Round each number.

    • 4,7824{,}782 rounds to 4,8004{,}800 because the tens digit is 88.
    • 2,1462{,}146 rounds to 2,1002{,}100 because the tens digit is 44.

  3. Subtract the rounded numbers.

4,800−2,100=2,7004{,}800-2{,}100=2{,}700

So, the estimated difference is:

2,700\boxed{2{,}700}

The estimate tells us that the exact difference should be close to 2,7002{,}700. It is useful for checking whether an exact subtraction answer makes sense.

Learn by doing: Estimate differences

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    Subtraction - Estimate Difference - 2 & 2 Digit

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