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

01 / LEARN

Understand the idea.

The digits change place value

Multiplication by ten makes each digit worth ten times as much. In $3.27 \times 10 = 32.7$ , three ones become three tens. Multiplying by one hundred moves each digit to a place worth one hundred times as much.

Division reverses this scaling. Dividing by one hundred makes each digit worth one hundredth as much, so zeros may be needed in empty places. Appending a trailing zero to a decimal alone does not scale it: $3.2 = 3.20$ .

Separate a multiple into factors

Split a multiple of a power of ten into convenient factors. Multiplying by $300 = 3 \times 100$ means multiply by three, then by one hundred. Dividing by $30 = 3 \times 10$ means divide by three, then by ten.

Check the direction of the change for positive numbers. Multiplying by a number greater than one increases the value; dividing by a number greater than one decreases it. Dividing by fifty is equivalent to dividing by one hundred then doubling.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Calculate $2.48 \times 300$ .

Worked solution

1
Factor the multiplier.
$300 = 3 \times 100$
The two factors separate the ordinary multiplication from place-value scaling.
2
Multiply by three.
$2.48 \times 3 = 7.44$
Three groups of 2.48 make 7.44.
3
Scale by one hundred.
$7.44 \times 100 = 744$
Each digit becomes worth one hundred times as much, completing multiplication by 300.

Answer

744.

EXAMPLE 02

Worked example 2

Calculate $36.9 \div 30$ .

Worked solution

1
Factor the divisor.
$30 = 3 \times 10$
Dividing by both factors in succession divides by their product.
2
Divide by three.
$36.9 \div 3 = 12.3$
Sharing 36.9 into three equal groups gives 12.3 in each.
3
Divide that result by ten.
$12.3 \div 10 = 1.23$
Every digit becomes worth one tenth as much.
4
Check with multiplication.
$1.23 \times 30 = 36.9$
The inverse operation returns to the starting value.

Answer

1.23.

03 / YOUR TURN

Try it yourself.

Check your understanding

Calculate $7.25 \div 100$ .

Show answer & reasoning

0.0725.

$7.25 \div 100 = 0.0725$ . The seven ones become seven hundredths; the two tenths become two thousandths and the five hundredths become five ten-thousandths.

Keep practising

6 worksheet questions · 10 marks

Open worksheet 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
$4.25 \times 2 \times 10 = 8.5 \times 10 = 85$ .
85.
Calculate $18.6 \div 60$ .
2 marks
$18.6 \div 6 \div 10 = 3.1 \div 10 = 0.31$ .
0.31.
Fifty identical pieces of ribbon are each 2.4 m long. Find their total length.
2 marks
$2.4 \times 5 \times 10 = 12 \times 10 = 120$ .
120 m.
Explain why $84 \div 20$ is the same as $84 \div 2 \div 10$ , then calculate it.
2 marks
$84 \div 2 = 42$ and $42 \div 10 = 4.2$ .
$20 = 2 \times 10$ , so dividing by each factor divides by 20 overall; the answer is 4.2.

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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 ↗

In this lesson

Understand the idea.

The digits change place value

Separate a multiple into factors

See the method in action.

Worked example 1

Factor the multiplier.

Multiply by three.

Scale by one hundred.

Worked example 2

Factor the divisor.

Divide by three.

Divide that result by ten.

Check with multiplication.

Try it yourself.

Check your understanding

Keep practising