Multiplying & Dividing Decimals — Grade 8 Maths (CAPS)

Counting decimal places when multiplying, the shift trick for dividing by a decimal, multiplying and dividing by 10, 100 and 1 000, 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 comma belongs.

1Multiplying by 10, 100 and 1 000

× 10 → comma moves 1 place right • × 100 → 2 places right • × 1 000 → 3 places right
÷ 10 → comma moves 1 place left, and so on.

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

1
3,65 × 100: move the comma 2 places right → 365.
Multiplying by 100 makes this number 100 times as large.
2
47,2 ÷ 10: move the comma 1 place left → 4,72.
Dividing by 10 makes this number one tenth as large.

2Multiplying two decimals: count the places

1. Ignore the commas 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 commas: 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 a positive number by a number between 0 and 1 makes the answer smaller: 0,4 × 0,3 = 0,12, which is smaller than both.

3Dividing by a decimal: shift both numbers

Dividing by a decimal is perfectly good mathematics — 1,44 ÷ 0,12 has an answer — it is just awkward to work out by hand. 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 divisor (the number you divide by) a whole number.

Worked ExampleCalculate: 1,44 ÷ 0,12

1
The divisor 0,12 has 2 decimal places, so multiply both numbers by 100.
This makes the divisor 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
The divisor 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 comma 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.

⚠️

Just as multiplying does not always make a number bigger, dividing does not always make it smaller. Dividing a positive number by a number between 0 and 1 makes it bigger: 6,4 ÷ 0,8 = 8 and 1,44 ÷ 0,12 = 12. Whether the answer grows or shrinks depends on what you multiply or divide by — there is no rule that works on its own.

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 × 1 000
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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