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Use compatible numbers
Choose nearby values that divide cleanly. For division, compatible numbers are often more useful than ordinary place-value rounding because they make the quotient obvious.
Estimated quotient ≈ compatible dividend ÷ compatible divisor
Worked example
For 42.3 ÷ 3.8, round to 42 ÷ 4. The estimate is about 10.5, so an answer near 11 is reasonable.
Check the scale of the answer
Before accepting an estimate, ask whether the result is in the right range. A divisor near 4 goes into a dividend near 40 about ten times.
Common mistakes
- Rounding the divisor to zero or an unusable value.
- Ignoring whether the estimated quotient is in a realistic range.
- Using incompatible numbers that are still hard to divide.
Frequently asked questions
What are compatible numbers?
They are nearby values chosen because they divide or multiply easily.
How do I estimate 42.3 divided by 3.8?
A simple estimate is 42 ÷ 4 = 10.5, so the exact answer should be near 11.
Is estimation useful for checking calculator answers?
Yes. A quick estimate is a strong way to catch misplaced decimals or data-entry mistakes.