Skill: Estimate differences of whole numbers

To estimate a difference, replace both numbers with nearby numbers that are easier to subtract. Round both numbers to the same place value, then subtract.

Example: Estimate $84{,}732-29{,}468$.

1. Choose a place value.
   Round both numbers to the nearest thousand.

2. Round each number.

   • $84{,}732$ rounds to $85{,}000$ because the hundreds digit is $7$.
   • $29{,}468$ rounds to $29{,}000$ because the hundreds digit is $4$.

3. Subtract the rounded numbers.

$$85{,}000-29{,}000=56{,}000$$

So,

$$84{,}732-29{,}468\approx 56{,}000.$$

4. Check that the estimate is reasonable.
   The exact difference is $55{,}264$, which is close to $56{,}000$. Also, rounding changed the first number up and the second number down, so the estimated difference should be a little larger than the exact difference. That makes $56{,}000$ plausible.