Multiplying and Dividing Decimals — KS3 Maths

To multiply decimals, remove the decimal points to create whole numbers, multiply, then reinsert the decimal point. To divide, convert the divisor to a whole number using powers of ten, then perform the division. Both skills are essential from Year 7 onwards.

Why decimal arithmetic matters at KS3

The DfE's KS3 mathematics programme of study requires pupils to multiply and divide with decimals, including in problems involving money, measurement, and proportion. The AQA GCSE Mathematics specification identifies decimal operations as a foundation for all number work, including percentages and standard form.

Multiplying decimals — the integer method

Key idea: convert both numbers to integers, multiply, then adjust the decimal point.

Step-by-step method

Count the total number of decimal places in both numbers combined.

Ignore the decimal points and multiply the integers.

Insert the decimal point so that the answer has the same total number of decimal places as the combined count in step 1.

Worked example 1 — 0.6 × 0.4

Total decimal places: 1 + 1 = 2

Integer multiplication: 6 × 4 = 24

Insert 2 decimal places: 0.24

Answer: 0.24

Worked example 2 — 3.7 × 1.2

Total decimal places: 1 + 1 = 2

Integer multiplication: 37 × 12 = 444

Insert 2 decimal places: 4.44

Answer: 4.44

Verify with an estimate: 3.7 × 1.2 ≈ 4 × 1 = 4. The answer 4.44 is close, so it is plausible.

Worked example 3 — 0.05 × 0.3

Total decimal places: 2 + 1 = 3

Integer multiplication: 5 × 3 = 15

Insert 3 decimal places: 0.015

Answer: 0.015

Multiplying by powers of ten

Multiplying by 10, 100, or 1000 moves every digit to the left by 1, 2, or 3 places respectively (equivalently, the decimal point moves right).

Multiplier | Effect | Example
× 10 | Decimal point moves 1 place right | 4.73 × 10 = 47.3
× 100 | Decimal point moves 2 places right | 4.73 × 100 = 473
× 1000 | Decimal point moves 3 places right | 4.73 × 1000 = 4730

Dividing decimals — converting the divisor

When dividing by a decimal, multiply both numbers by a power of 10 to make the divisor (the number you are dividing by) a whole number.

a ÷ b = (a × 10) ÷ (b × 10) — the value does not change.

Worked example 4 — 7.2 ÷ 0.4

Multiply both by 10: 72 ÷ 4 = 18

Answer: 18

Worked example 5 — 3.6 ÷ 0.06

Multiply both by 100: 360 ÷ 6 = 60

Answer: 60

Worked example 6 — 0.48 ÷ 0.8

Multiply both by 10: 4.8 ÷ 8 = 0.6

Answer: 0.6

Dividing by powers of ten

Dividing by 10, 100, or 1000 moves every digit to the right (equivalently, the decimal point moves left).

Divisor | Effect | Example
÷ 10 | Decimal point moves 1 place left | 36.5 ÷ 10 = 3.65
÷ 100 | Decimal point moves 2 places left | 36.5 ÷ 100 = 0.365
÷ 1000 | Decimal point moves 3 places left | 36.5 ÷ 1000 = 0.0365

Using estimation to check answers

Always estimate before you calculate. Replace each decimal with a nearby, easy number and check that your answer is in the right ballpark.

Worked example 7 — estimate to check 2.87 × 4.3

Estimate: 3 × 4 = 12

Calculation: 287 × 43 = 12,341; 4 decimal places → 12.341 ≈ 12.3

The answer 12.341 is close to the estimate of 12, so it is correct.

Common mistakes to avoid

Mistake | Example of error | Correct approach
Wrong decimal place count | 0.6 × 0.4 = 2.4 (only counted one decimal place) | Count ALL decimal places: 1 + 1 = 2, so answer = 0.24
Not adjusting divisor and dividend equally | 7.2 ÷ 0.4 → converting only dividend: 72 ÷ 0.4 | Multiply BOTH by 10: 72 ÷ 4 = 18
Moving the decimal the wrong way when dividing by 10 | 3.5 ÷ 10 = 35 | Dividing makes the number smaller: 3.5 ÷ 10 = 0.35
Skipping estimation | Writing 0.244 without checking plausibility | Always estimate first (e.g., 3.7 × 1.2 ≈ 4)

Frequently asked questions

How do I multiply two decimals together without a calculator?

Remove both decimal points to form integers, then multiply those integers using long multiplication or any written method you know. Count the total number of decimal places in the original two numbers and reinsert the decimal point in the answer so it has the same total. For example, 2.4 × 0.3: integers are 24 × 3 = 72; total decimal places = 1 + 1 = 2; answer = 0.72.

How do I divide a decimal by a decimal?

Multiply both the dividend and the divisor by the same power of 10 so that the divisor becomes a whole number. This does not change the value of the division. For example, 4.5 ÷ 0.9: multiply both by 10 to get 45 ÷ 9 = 5.

Why does multiplying by 10 move the decimal point one place to the right?

Our number system is base ten: each position is worth ten times the position to its right. Multiplying by 10 makes every digit worth ten times as much, so each digit moves one column to the left — which is the same as the decimal point moving one place to the right. Dividing by 10 does the opposite.

How can I check my answer when multiplying decimals?

Estimate first by rounding each decimal to the nearest whole number or simple fraction. After calculating, compare your answer to the estimate. If they are wildly different, you have likely misplaced the decimal point. Also check: multiplying two numbers each less than 1 should give an answer smaller than either of them.

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