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Use 42 ÷ 4
The divisor 3.8 is close to 4, and 42.3 is close to 42. That creates a division problem that is easy to estimate mentally.
42.3 ÷ 3.8 ≈ 42 ÷ 4 = 10.5
Worked example
The exact quotient is a little above 11. Since 3.8 is slightly less than 4, dividing by 3.8 produces a result slightly larger than 42 ÷ 4.
Use the estimate to check a decimal answer
If a calculator returned 1.1 or 110, the estimate near 11 would immediately show that the decimal point is wrong.
Common mistakes
- Rounding 3.8 down to 3 when 4 is much closer.
- Ignoring the direction of the rounding.
- Mistaking 10.5 for the exact quotient.
Frequently asked questions
What is a reasonable estimate for 42.3 ÷ 3.8?
About 10.5 to 11.
Why is the exact answer a little above 10.5?
Because the actual divisor 3.8 is smaller than 4.
Can I use 40 ÷ 4 instead?
Yes. That gives 10, which is a rougher but still reasonable estimate.