You can multiply decimals and round them. Put the two together and you have a fast check that catches a decimal point in the wrong place.
Key idea
Round each factor to a whole number (or another easy number) and multiply. The exact answer should be close to the estimate. Use the estimate to place the decimal point.
Why it works
The digits of $2.4 \times 3.1$ are the digits of $24 \times 31 = 744$. Where does the point go: $0.744$, $7.44$, $74.4$? Since $2.4$ is about 2 and $3.1$ is about 3, the product is about $2 \times 3 = 6$. Only $7.44$ is close to 6.
Worked examples
Worked example: Place the point
$3.8 \times 5.2$ has the digits 1976. Where does the point go?
- Estimate: $4 \times 5 = 20$.
- The choices are $0.1976$, $1.976$, $19.76$, $197.6$. Only $19.76$ is near 20.
Answer: $19.76$
Worked example: Is it reasonable?
Is $0.48 \times 9.6 = 46.08$ reasonable?
- $0.48$ is about $0.5$, a half, and $9.6$ is about 10.
- Half of 10 is 5. $46.08$ is far from 5.
Answer: No. The product is $4.608$.
Common mistake
Accepting an answer like $2.4 \times 3.1 = 74.4$ without comparing it to $2 \times 3$. Check every decimal product with a whole-number estimate; a misplaced point is off by 10 times or more, which an estimate shows right away.