Multiplying & Dividing Decimals

Counting decimal places when multiplying, the shift trick for dividing by a decimal, multiplying and dividing by 10, 100 and 1000, and estimating the answer first — worked examples, a worksheet with memo and a quiz.

Multiplying and dividing decimals looks harder than it is. In both cases you do an ordinary whole-number calculation and then work out where the point belongs.

1Multiplying by 10, 100 and 1000

× 10 → point moves 1 place right • × 100 → 2 places right • × 1000 → 3 places right
÷ 10 → point moves 1 place left, and so on.

Worked ExampleCalculate: 3,65 × 100 and 47,2 ÷ 10

1
3,65 × 100: move the point 2 places right → 365.
Multiplying makes the number bigger.
2
47,2 ÷ 10: move the point 1 place left → 4,72.
Dividing makes it smaller.

2Multiplying two decimals: count the places

1. Ignore the points and multiply as whole numbers.
2. Count the total number of decimal places in the question.
3. Put that many decimal places in the answer.

Worked ExampleCalculate: 0,4 × 0,3

1
Ignore the points: 4 × 3 = 12.
Do the easy whole-number sum first.
2
Count decimal places in the question: 0,4 has 1 and 0,3 has 1 → 2 in total.
3
Put 2 decimal places in the answer: 0,12.
12 becomes 0,12.

Worked ExampleCalculate: 2,5 × 1,2

1
Whole numbers: 25 × 12 = 300.
2
Decimal places: 1 + 1 = 2.
3
300 with 2 decimal places → 3,00 = 3.
Check by estimating: 2,5 × 1,2 is a bit more than 2,5 — and 3 is sensible.

⚠️

A very common error is thinking multiplying always makes numbers bigger. Multiplying by a number less than 1 makes the answer smaller: 0,4 × 0,3 = 0,12, which is smaller than both.

3Dividing by a decimal: shift both numbers

You cannot divide by a decimal directly, so change the question into an easier one with the same answer: multiply both numbers by 10, 100 or whatever it takes to make the divider a whole number.

Worked ExampleCalculate: 1,44 ÷ 0,12

1
The divider 0,12 has 2 decimal places, so multiply both numbers by 100.
This makes the divider a whole number.
2
1,44 × 100 = 144 and 0,12 × 100 = 12.
Doing the same to both keeps the answer unchanged.
3
Now 144 ÷ 12 = 12.
An ordinary whole-number division.

Worked ExampleCalculate: 6,4 ÷ 0,8

1
Divider 0,8 has 1 decimal place → multiply both by 10.
2
64 ÷ 8 = 8.
3
Answer: 8.
Sensible: there are eight 0,8s in 6,4.

💡

Estimate first to place the point safely: 6,4 ÷ 0,8 is roughly 6 ÷ 1 = 6, so an answer of 8 is believable but 0,8 or 80 would not be.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
4,27 × 10
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42,7
2
0,85 × 1000
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850
3
63,5 ÷ 100
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0,635
4
0,6 × 0,4
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6×4 = 24, 2 dp → 0,24
5
1,5 × 0,3
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15×3 = 45, 2 dp → 0,45
6
2,4 × 1,5
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24×15 = 360, 2 dp → 3,6
7
0,9 ÷ 0,3
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×10 both → 9 ÷ 3 = 3
8
8,4 ÷ 0,4
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×10 both → 84 ÷ 4 = 21
9
2,25 ÷ 0,15
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×100 both → 225 ÷ 15 = 15
10
1 kg of rice costs R24,50. What do 2,5 kg cost?
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24,50 × 2,5 = R61,25