Lumen🪙 0

Multiplying decimals

📖 Learn🎬 Guided Practice✏️ Practice

Decimals

Multiplying decimals

Ignore the decimal point, do an ordinary multiplication, then put the point back by counting digits.

Count the decimal places in — put the same number back1 · ignore the point476 × 37 = 176122 · count the places3.7 has 1476 × 3.7 = 1761.21 place0.002 × 4 → 3 places → 0.008
1.80 and 1.8 are the same — the trailing zero adds nothing.

The method

To multiply a decimal by a whole number: 1. Work out the multiplication WITHOUT the decimal point. 2. Put the point back in the answer. There must be the same number of digits after the point in the ANSWER as there were in the QUESTION.

Mental examples

0.002 × 4 2 × 4 = 8. The question has three digits after the point, so the answer must too: 0.008 30 × 0.06 30 × 6 = 180. The question has two digits after the point, so: 1.80 You can write 1.80 as 1.8, because the trailing zero is not needed.

A written example

476 × 3.7 First ignore the point and work out 476 × 37: 476 × 7 = 3332 476 × 30 = 14280 3332 + 14280 = 17612 The question has ONE digit after the point, so the answer needs one: 476 × 3.7 = 1761.2

Worked examples

0.002 × 4

  1. Ignore the point: 2 × 4 = 8.
  2. The question has 3 digits after the point, so the answer needs 3.

Answer: 0.008

30 × 0.06

  1. 30 × 6 = 180.
  2. The question has 2 digits after the point.

Answer: 1.80, usually written 1.8

476 × 3.7

  1. Ignore the point: 476 × 37.
  2. 476 × 7 = 3332 and 476 × 30 = 14 280.
  3. 3332 + 14 280 = 17 612.
  4. One digit after the point in the question.

Answer: 1761.2

Why the trailing zero can go

  1. 1.80 and 1.8 are the same value.
  2. The final zero adds nothing.

Answer: 1.8

0.4 × 0.2

  1. 4 × 2 = 8.
  2. The question has 2 digits after the point altogether.

Answer: 0.08

Counting the digits

  1. Count every digit after a point in the QUESTION.
  2. The answer must have the same number.

Answer: That is the whole rule

Where you see this in real life

  • Seven items at £1.35 each: work out 7 × 135 = 945, then place the point — £9.45.
  • A 3.7 m plank cut into 476 pieces… or 476 planks of 3.7 m: the same 1761.2 m either way.

Key words

Decimal place
a digit position after the decimal point
Product
the result of a multiplication
Trailing zero
a zero at the end of a decimal that can be dropped
Estimate
a rough answer used to check a calculation
🎬 Try Guided Practice →Skip to Practice →