You can multiply a decimal by a whole number. When both factors are decimals, the new question is the size of the unit: what do you get from tenths times tenths?
Key idea
Multiply as if there were no decimal points. Then count the decimal places in both factors together; the product has that many decimal places. $0.3 \times 0.2 = 0.06$.
Why it works
$0.3 \times 0.2$ means 3 tenths of 2 tenths. A tenth of a tenth is a hundredth (cut a square into 10 strips, then each strip into 10 pieces: 100 pieces). So the product is $3 \times 2 = 6$ hundredths. In fractions: $\frac{3}{10} \times \frac{2}{10} = \frac{6}{100}$. Tenths times tenths make hundredths, so 1 place and 1 place give 2 places.
Worked examples
Worked example: Tenths times tenths
Find $0.3 \times 0.2$.
- $3 \times 2 = 6$.
- Each factor has 1 decimal place, so the product has 2.
- 6 hundredths: write a 0 in the tenths place.
Answer: $0.06$
Worked example: Bigger factors
Find $1.4 \times 2.3$.
- $14 \times 23 = 322$.
- 1 decimal place + 1 decimal place = 2.
- $3.22$. Estimate: $1 \times 2 = 2$ and $1.5 \times 2.5$ is under 4. It fits.
Answer: $3.22$
Common mistake
Lining up the points as in adding and writing $0.3 \times 0.2 = 0.6$. Check: when both factors are less than 1, the product is smaller than each of them. $0.6$ is bigger than $0.3$, so it cannot be right.