Multiplying and Dividing Decimals

What you will learn

• Multiply and divide decimals by $10$, $100$ and $1000$.
• Multiply decimals by whole numbers and by other decimals.
• Divide decimals by whole numbers and by decimals.

Before you start: you should know decimal place value and be able to multiply whole numbers. See Decimals Explained and Multiplying Larger Numbers.

The idea

Multiplying by $10$ makes every digit worth ten times more, so each digit moves one place to the left. The decimal point stays where it is.

Dividing by $10$ moves each digit one place to the right. Multiplying by $100$ moves two places, and so on.

Multiplying decimals

1. Ignore the decimal points and multiply the whole numbers.
2. Count the decimal places in both numbers together.
3. Put that many decimal places in the answer.

For $0.3 \times 0.4$: $3 \times 4 = 12$, and there are $2$ places, so $0.12$. An area model shows why: a square cut into $10$ by $10$ small squares, with $3$ columns and $4$ rows overlapping in $12$ of the $100$.

Dividing decimals

Dividing by a whole number works like normal division, keeping the point in place. To divide by a decimal, multiply both numbers by the same power of ten until the divisor is whole. $1.2 \div 0.4$ becomes $12 \div 4 = 3$. The answer does not change, because you scaled both numbers equally.

Estimate to check

$2.4 \times 3$ is about $2 \times 3 = 6$, and the exact answer is $7.2$. A misplaced point would give $0.72$ or $72$, which the estimate rules out.

Worked examples

Example 1: Multiply

Work out $0.6 \times 0.04$.

1. $6 \times 4 = 24$.
2. $0.6$ has $1$ decimal place and $0.04$ has $2$, so $3$ in total.
3. The answer is $0.024$.

Answer: $0.024$

Example 2: Divide by a decimal

Work out $4.8 \div 0.6$.

1. Multiply both by $10$: $48 \div 6$.
2. $48 \div 6 = 8$.

Answer: $8$

Example 3: Money

Four notebooks cost £$2.35$ each. What is the total?

1. $235 \times 4 = 940$.
2. $2.35$ has $2$ decimal places, so the answer is $9.40$.

Answer: £$9.40$

Watch out: multiplying does not always make a number bigger. $0.5 \times 0.5 = 0.25$ is smaller than $0.5$.

Why it matters

Prices per kilogram, fuel costs, speeds and scale factors all involve multiplying and dividing decimals. Knowing how the point behaves lets you check a calculator answer and spot a slip by a factor of ten.