Multiplication/division by multiples of powers of ten | Year 6

01 / LEARN

The idea, step by step

The digits change place value

Multiplying by 10 makes every digit worth ten times as much. For example, 3.27 becomes 32.7: the 3 ones become 3 tens. Multiplying by 100 makes every digit worth one hundred times as much.

Division reverses that change. In 32.7÷10=3.27, each digit has one tenth of its previous value. Use zeros when a place needs filling, but do not add zeros to the end of a decimal and assume that its value has changed.

Separate a multiple into factors

To multiply by 300, you can multiply by 3 and then by 100. To divide by 30, divide by 3 and then by 10. Both steps together perform the original operation.

Choose a route with easy intermediate results. To divide by 50, dividing by 100 and then multiplying by 2 gives the same result, because 50 is half of 100. Check whether the answer should be larger or smaller than the starting positive number.

A common trap

Writing $3.2 \times 10 = 3.20$ .

Instead: 3.20 equals 3.2, so no multiplication has happened. Ten times 3.2 is 32.

02 / WORKED EXAMPLES

See the thinking

Example 1

Worked example 1

Calculate $2.48 \times 300$ .

Separate 300 into 3×100.
2.48×3=7.44. Then 7.44×100=744.
Multiplying by 300 should give a much larger number than 2.48.

744.

Example 2

Worked example 2

Calculate $36.9 \div 30$ .

Separate 30 into 3×10.
36.9÷3=12.3. Divide by 10 again: 12.3÷10=1.23.
Check: 1.23×30=36.9.

1.23.

Check your understanding

Calculate $7.25 \div 100$ .

Show answer

0.0725.

Each digit is worth one hundredth as much; the 7 ones become 7 hundredths.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Calculate $0.46 \times 1, 000$ .
1 mark
Calculate $73.5 \div 100$ .
1 mark
Calculate $4.25 \times 20$ .
2 marks
Calculate $18.6 \div 60$ .
2 marks
Fifty identical pieces of ribbon are each 2.4 m long. Find their total length.
2 marks
Explain why $84 \div 20$ is the same as $84 \div 2 \div 10$ , then calculate it.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Calculate $0.46 \times 1, 000$ .
1 mark
Each digit has 1,000 times its original value.
460.
Calculate $73.5 \div 100$ .
1 mark
Divide the value by 100.
0.735.
Calculate $4.25 \times 20$ .
2 marks
4.25×2×10=8.5×10=85.
85.
Calculate $18.6 \div 60$ .
2 marks
18.6÷6÷10=3.1÷10=0.31.
0.31.
Fifty identical pieces of ribbon are each 2.4 m long. Find their total length.
2 marks
2.4×5×10=12×10=120.
120 m.
Explain why $84 \div 20$ is the same as $84 \div 2 \div 10$ , then calculate it.
2 marks
84÷2=42 and 42÷10=4.2.
20=2×10, so dividing by each factor divides by 20 overall; the answer is 4.2.

Checking saved progress…

Continue learning

Estimating decimal calculations

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Addition/subtraction; multiplication/division by multiples of powers of ten; estimation.

Official curriculum source ↗

Back to Decimals