You can add decimals, and you know how multiplying by 10 moves digits. Multiplying a decimal by a whole number is repeated adding of tenths or hundredths.
Key idea
Think of the decimal as a count of tenths or hundredths. Multiply that count by the whole number, then write the result in the same unit: $4 \times 0.3$ is $4 \times 3$ tenths $= 12$ tenths $= 1.2$.
Why it works
$4 \times 0.3$ means four groups of 3 tenths. That is 12 tenths. Ten tenths make one whole, so 12 tenths is 1 whole and 2 tenths: $1.2$. Units stay units: tenths times a whole number are still tenths.
Worked examples
Worked example: Tenths
Find $4 \times 0.3$.
- $0.3$ is 3 tenths.
- $4 \times 3 = 12$, so the product is 12 tenths.
- 12 tenths $= 1.2$.
Answer: $1.2$
Worked example: Hundredths
Find $6 \times 2.35$.
- $2.35$ is 235 hundredths.
- $6 \times 235 = 1{,}410$ hundredths.
- 1,410 hundredths $= 14.10 = 14.1$.
- Estimate: $6 \times 2 = 12$, and $6 \times 2.5 = 15$. The answer is between.
Answer: $14.1$
Common mistake
Losing track of the unit and writing $6 \times 2.35 = 141$ or $1.41$. Check with an estimate: $2.35$ is a bit more than 2, so six of them are a bit more than 12.