Multiplying decimals

Multiply first, place the point second

To multiply decimals:

1. Ignore the decimal points and multiply as whole numbers.
2. Count the total number of decimal places in both factors.
3. Place the decimal point so the product has that many decimal places.

Example: 2.3 × 1.4

• 23 × 14 = 322
• Decimal places: 1 + 1 = 2
• Product: 3.22

Why counting works

2.3 × 1.4 = 23/10 × 14/10 = 322/100 = 3.22. Each decimal place is a division by 10, so the places add up.

Check with an estimate

Always estimate: 2.3 × 1.4 ≈ 2 × 1.5 = 3. The answer 3.22 is reasonable; 32.2 or 0.322 would not be.

More examples

When the product has too few digits, add zeros in front: 0.05 × 0.3 → 15 needs 3 places → 0.015.

Trailing zeros after the point can be dropped at the end: 3.00 = 3.

Multiplying by powers of 10

Multiplying by a power of 10 shifts every digit to a higher place value. The decimal point appears to move right:

Multiplying by 0.1, 0.01 … moves the point left: 3.456 × 0.1 = 0.3456.

Does multiplying make it bigger?

Multiplying by a decimal less than 1 gives a smaller answer: 8 × 0.5 = 4. That’s "half of 8".

Real-life examples

• 3.5 kg of apples at $2.40/kg: 3.5 × 2.40 = $8.40
• A rectangle 4.2 m by 2.5 m: area = 10.5 m²

Worked examples

Example 1: 0.4 × 0.3

4 × 3 = 12; 2 decimal places → 0.12.

Example 2: 6.7 × 0.08

67 × 8 = 536; 3 decimal places → 0.536.

Example 3: 15.2 × 100

Move the point 2 right → 1,520.

Common mistakes

• Lining up decimal points as in addition. For multiplication, you don’t need to.
• Counting decimal places in only one factor.
• Forgetting leading zeros: 0.2 × 0.3 is 0.06, not 0.6.

Try it yourself

1. 1.5 × 0.6
2. 3.14 × 2
3. 0.07 × 0.4
4. 2.45 × 1,000
5. Gas costs $1.62 per litre. How much for 40 L?

Answers: 1) 0.9 2) 6.28 3) 0.028 4) 2,450 5) $64.80

Quick recap

• Multiply as whole numbers, then count decimal places.
• Estimate to check where the point goes.
• Multiplying by a power of 10 moves the point right.