Multiplying Decimals

The big idea

Multiplying decimals looks tricky because of the points, but the trick is simple: pretend the points are not there, multiply the whole numbers, then put one point back in the answer. The only new skill is knowing where the point goes.

The three-step method

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total decimal places in the two numbers you started with.
3. Place the decimal point in your answer so it has that many decimal places.

Worked example 1: 0.3 × 0.4

1. Ignore points → multiply 3 × 4 = 12.
2. Count places: 0.3 has 1 place, 0.4 has 1 place → total 2.
3. Put the point so the answer has 2 decimal places → 0.12.

Check it makes sense: 0.3 and 0.4 are both small parts, so the answer should be tiny — and 0.12 is. ✅

Worked example 2: 2.5 × 0.6

1. Ignore points → 25 × 6 = 150.
2. Count places: 2.5 has 1, 0.6 has 1 → total 2.
3. Answer needs 2 decimal places: 150 → 1.50 = 1.5.

Worked example 3: 1.24 × 0.3

1. Ignore points → 124 × 3 = 372.
2. Count places: 1.24 has 2, 0.3 has 1 → total 3.
3. Place the point for 3 decimal places: 372 → 0.372.

Estimate first to place the point

The most common mistake is putting the point in the wrong spot. Beat it by estimating with rounded numbers before you start.

Example: 4.9 × 3.1

• Round to 5 × 3 = 15, so the answer is about 15.
• Now compute exactly: 49 × 31 = 1519, total decimal places = 1 + 1 = 2 → 15.19.
• 15.19 is close to 15, so the point is correct. ✅

If your exact answer came out as 1.519 or 151.9, the estimate would warn you instantly.

Why multiplying can make numbers smaller

Multiply by	Effect	Example
more than 1 (e.g. 3)	answer gets bigger	8 × 3 = 24
exactly 1	answer stays the same	8 × 1 = 8
less than 1 (e.g. 0.5)	answer gets smaller	8 × 0.5 = 4
much less than 1 (e.g. 0.1)	answer gets much smaller	8 × 0.1 = 0.8

Multiplying by 0.5 is the same as taking half; multiplying by 0.1 is the same as dividing by 10. This surprises many students, so keep it in mind.

Why the place-value rule works

Each decimal place is a hidden "divide by 10". Writing 0.3 is really 3 ÷ 10, and 0.4 is 4 ÷ 10. So:

0.3 × 0.4 = (3 ÷ 10) × (4 ÷ 10) = (3 × 4) ÷ 100 = 12 ÷ 100 = 0.12

Two "divide by 10"s combine into "divide by 100", which is exactly two decimal places. That is why you add the decimal places.

Try it yourself: shopping cart

Price out a pretend shop using decimals:

• 3 apples at $0.45 each → 3 × 0.45 = ?
• 2.5 kg of rice at $1.20 per kg → 2.5 × 1.20 = ?
• 0.6 litres of juice at $2.50 per litre → 0.6 × 2.50 = ?

Estimate each total first, then work it out exactly and check the point is in a sensible place.

Why this matters

Multiplying decimals powers real-life calculations: prices, areas, measurements and scaling. It pairs naturally with adding and subtracting decimals and the place-value ideas in decimals explained.