Step 1: Ignore the decimal point and multiply as whole numbers. Step 2: Count decimal places in the original. Step 3: Put the decimal point back.
Multiply the numbers as if there were no decimal point at all, then place a decimal point back into your answer so it has the same number of digits after it as the original decimal did. Multiplying by a whole number doesn't change how many decimal places the answer needs.
Example 1 — Calculate \(3.47 \times 4\)
Step 1
Ignore the decimal: treat 3.47 as 347.
Step 2
Multiply: \(347 \times 4 = 1388\).
Step 3
3.47 has 2 decimal places, so place the point 2 from the right: \(\mathbf{13.88}\)
Example 2 — Calculate \(6.5 \times 8\)
Step 1
Ignore the decimal: treat 6.5 as 65.
Step 2
Multiply: \(65 \times 8 = 520\).
Step 3
6.5 has 1 decimal place → answer has 1 d.p.: \(\mathbf{52.0} = 52\)
Check with estimation: \(3.47 \times 4 \approx 3.5 \times 4 = 14\). Answer 13.88 is close — looks right!
✓ Quick Check 1 — Decimal × Whole Number
Question 1 of 10
Decimal × Decimal — Count Total Decimal Places
Total decimal places in the answer = decimal places in first number + decimal places in second number
When both numbers are decimals, count the total decimal places across both numbers. Multiply as whole numbers, then insert the decimal point so the answer has that many decimal places.
💡 Why this works: a decimal is really a fraction in disguise — 1 decimal place means tenths (÷10), 2 places means hundredths (÷100). So \(1.4 \times 0.3 = \frac{14}{10} \times \frac{3}{10} = \frac{42}{100} = 0.42\). Multiplying two "÷10"s together gives a "÷100" — that's why the decimal places add rather than multiply or average.
Example 3 — Calculate \(1.4 \times 0.3\)
Step 1
Count decimal places: 1.4 has 1, 0.3 has 1. Total = 2 decimal places.
Step 2
Multiply as whole numbers: \(14 \times 3 = 42\).
Step 3
Place point 2 from the right: 42 → \(\mathbf{0.42}\)
Example 4 — Calculate \(2.5 \times 1.4\)
Step 1
Total decimal places: \(1 + 1 = 2\).
Step 2
\(25 \times 14 = 350\).
Step 3
Place point: \(350\) → 2 d.p. → \(\mathbf{3.50} = 3.5\)
⚠ Common mistake: Forgetting to count decimal places from BOTH numbers. \(1.4 \times 0.3\) needs 2 decimal places, not 1.
✓ Quick Check 2 — Decimal × Decimal
Question 1 of 10
Estimation to Check — and Real-Life Applications
Always estimate first to check your answer is roughly right. Round each number to 1 significant figure, multiply, then compare to your calculated answer. If they're very different, recheck.
Example 5 — A room is 4.5 m × 3.2 m. Find the area.
Place point (3 d.p.): \(429000 \to \mathbf{£429.00}\). Close to estimate ✓
✓ Quick Check 3 — Estimation and Real-Life Multiplication
Question 1 of 10
Practice: Decimal Multiplication
Estimate first, then calculate. Type your answer, then click Check.
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Question
Answer
Result
1
\(2.6 \times 5\)
2
\(0.8 \times 0.9\)
3
\(1.25 \times 4\)
4
\(3.4 \times 6\)
5
\(0.5 \times 0.5\)
6
\(7.2 \times 3\)
7
\(2.25 \times 4\)
8
\(0.6 \times 1.5\)
9
\(12.5 \times 0.2\)
10
\(4.8 \times 2.5\)
⚠ Things to Watch Out For
Not removing the decimal before multiplying: Treat the decimals as whole numbers first: 1.4 × 0.3 → 14 × 3 = 42. Then place the decimal point back.
Counting decimal places incorrectly: Count the total decimal places in BOTH numbers. 1.4 (1 d.p.) × 0.3 (1 d.p.) = 0.42 (2 d.p.). The answer has the combined number of decimal places.
Not estimating first: 1.4 × 0.3 ≈ 1 × 0.3 = 0.3. If your answer is 4.2 or 0.042, you know the decimal placement is wrong.
Decimal × decimal gives a larger number: FALSE. Multiplying by a decimal less than 1 always makes the number SMALLER. 5 × 0.2 = 1, not 10.
Forgetting trailing zeros: 2.0 × 3.0: 20 × 30 = 600, with 2 decimal places → 6.00. Don't drop the trailing zeros until you've correctly placed the decimal.