Multiples/powers of ten | Year 4

01 / LEARN

Understand the idea.

Each place is ten times the place to its right

Multiplying by $10$ makes every digit's value ten times as large. In $34 \times 10 = 340$ , three tens become three hundreds and four ones become four tens. The zero holds the empty ones place; it is a result of the change in value.

Multiplying by $100$ applies this change twice. Each digit takes a value two places higher: $34 \times 100 = 3.400$ . Follow the digits' values in a place-value chart instead of treating the zeroes as an unexplained writing trick.

Reverse the scaling and use known facts

Division by $10$ reverses multiplication by $10$ . Since $34 \times 10 = 340$ , we know $340 \div 10 = 34$ . Dividing $3.400$ by $100$ reverses two tenfold changes and also gives $34$ . Use multiplication to check which scale was reversed.

Use a basic fact to multiply a multiple of ten or one hundred. In $3 \times 200$ , count three groups of two hundreds. The fact $3 \times 2 = 6$ gives six hundreds, or $600$ . Keep naming the units so the total has the correct size.

Scaling the fact 3 × 2 = 6
Calculation	Value
3 × 2	6
3 × 20	60
3 × 200	600

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Multiply by one hundred

Find 47 × 100.

Worked solution

1
Separate the tens and ones.
$47 = 40 + 7$
Both place-value parts will be made one hundred times as large.
2
Scale each part by one hundred.
$\begin{aligned} 40 \times 100 & = 4.000 \\ 7 \times 100 & = 700 \end{aligned}$
Four tens become four thousands, and seven ones become seven hundreds.
3
Combine the new values.
$4.000 + 700 = 4.700$
The two scaled parts give the full product of 47 and 100.

Answer

4,700.

EXAMPLE 02

Use a basic fact

Find 6 × 40 and check it by division.

Worked solution

1
Recall the fact for six groups of four.
$6 \times 4 = 24$
The digit 4 in 40 counts tens, so this fact gives the number of tens.
2
Convert twenty-four tens into a number.
$24 \times 10 = 240$
Six groups of forty contain twenty-four tens.
3
Check by division.
$240 \div 6 = 40$
Dividing the total among six groups recovers forty in each group.

Answer

240.

03 / YOUR TURN

Try it yourself.

Check your understanding

Find 4,300 ÷ 100.

Show answer & reasoning

43.

The answer is $43$ , because $43 \times 100 = 4.300$ . Division by one hundred reverses the scaling of every digit by one hundred.

Keep practising

6 worksheet questions · 7 marks

Open worksheet Worked solutions

Read the questions online

Find $28 \times 10$ .
1 mark
Find $63 \times 100$ .
1 mark
Find $5.600 \div 100$ .
1 mark
Find $7 \times 80$ .
1 mark
A carton holds 100 cards. How many cards are in 24 cartons?
1 mark
A learner says $9 \times 300 = 270$ . Explain and correct the place-value error.
2 marks

Read the worked solutions

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

Find $28 \times 10$ .
1 mark
Two tens become two hundreds; eight ones become eight tens.
280.
Find $63 \times 100$ .
1 mark
$63 \times 10 = 630$ , then $630 \times 10 = 6.300$ .
6,300.
Find $5.600 \div 100$ .
1 mark
$56 \times 100 = 5.600$ .
56.
Find $7 \times 80$ .
1 mark
$7 \times 8 = 56$ ; $56 tens = 560$ .
560.
A carton holds 100 cards. How many cards are in 24 cartons?
1 mark
$24 \times 100 = 2.400$ .
2,400 cards.
A learner says $9 \times 300 = 270$ . Explain and correct the place-value error.
2 marks
$9 \times 3 = 27$ , but these are hundreds, not tens.
$27 hundreds = 2.700$ .
$9 \times 300 = 2.700$ .

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Facts to 10×10; related division; larger calculations; multiples/powers of ten; efficient strategies.

Official curriculum source ↗

In this lesson

Understand the idea.

Each place is ten times the place to its right

Reverse the scaling and use known facts

See the method in action.

Multiply by one hundred

Separate the tens and ones.

Scale each part by one hundred.

Combine the new values.

Use a basic fact

Recall the fact for six groups of four.

Convert twenty-four tens into a number.

Check by division.

Try it yourself.

Check your understanding

Keep practising