Place value and powers of ten | Year 7

01 / LEARN

Understand the idea.

Each position has a value

A digit's place value tells how much it contributes. In $4.072.305$ , the 7 counts ten-thousands, so its contribution is $70.000$ . Each place is worth ten times the place immediately to its right.

Read the table one column at a time. Zero keeps an empty place: without the zero in the hundred-thousands column, the later digits would occupy different places. Expanded form adds the contributions of the non-zero digits.

Reading 4,072,305
Millions	Hundred-thousands	Ten-thousands	Thousands	Hundreds	Tens	Ones
4	0	7	2	3	0	5

Powers of ten

A power of ten abbreviates repeated multiplication: $10^{3}$ has three factors of 10. Multiplying by $10^{3}$ makes each digit's contribution one thousand times as large; dividing by it reverses that scaling.

Track place values rather than using a rule about adding or removing zeros. For instance, dividing $46.000$ by 1,000 counts how many thousands it contains, giving 46. The decimal point separates whole-number places from fractional places.

10^{1} = 10, 10^{2} = 100, 10^{3} = 1000

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Explain a large number

Write 5,308,042 in expanded form.

Worked solution

1
Identify the occupied places.
$\begin{aligned} 5 \times 1.000.000 & = 5.000.000 \\ 3 \times 100.000 & = 300.000 \\ 8 \times 1.000 & = 8.000 \end{aligned}$
The digit gives the count; the column gives the size of each unit.
2
Include the tens and ones.
$4 \times 10 = 40, 2 \times 1 = 2$
The zero hundreds and ten-thousands contribute nothing, while retaining their places.
3
Add the contributions.
$5.308.042 = 5.000.000 + 300.000 + 8.000 + 40 + 2$
Expanded form represents the same number as a sum of place-value amounts.

Answer

$5.000.000 + 300.000 + 8.000 + 40 + 2$

EXAMPLE 02

Scale in two stages

Calculate $3640 \times 100$ , then divide that result by 1,000.

Worked solution

1
Multiply the original number by 100.
$3640 \times 100 = 364.000$
Every digit now contributes one hundred times its original value.
2
Divide that result by 1,000.
$364.000 \div 1000 = 364$
There are 364 groups of one thousand in 364,000.
3
Check the combined scaling.
$\frac{100}{1000} = \frac{1}{10}, 3640 \div 10 = 364$
The two operations together make the original value one tenth as large.

Answer

364

03 / YOUR TURN

Try it yourself.

Check your understanding

What does the 8 represent in 583,214?

Show answer & reasoning

80,000

In $583.214$ , the 8 occupies the ten-thousands place. Its contribution is $8 \times 10.000 = 80.000$ .

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

What is the value of the 6 in 2,604,815?
2 marks
Write 7,020,409 in expanded form.
2 marks
Calculate $48 \times 1000$ .
2 marks
Calculate $930.000 \div 100$ .
2 marks
Write the number with 4 hundred-thousands, 7 thousands, 2 tens and 6 ones.
2 marks
Use each digit 0, 2, 4, 6, 7 and 9 once to make the greatest six-digit number.
2 marks

Read the worked solutions

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

What is the value of the 6 in 2,604,815?
2 marks
The 6 is in the hundred-thousands position.
$6 \times 100.000 = 600.000$ .
600,000
Write 7,020,409 in expanded form.
2 marks
Read each non-zero digit with its position.
There are 7 millions, 2 ten-thousands, 4 hundreds and 9 ones.
$7.000.000 + 20.000 + 400 + 9$
Calculate $48 \times 1000$ .
2 marks
Multiplication by 1,000 scales each digit by 1,000.
$48 \times 1000 = 48.000$ .
48,000
Calculate $930.000 \div 100$ .
2 marks
Group the number into hundreds.
$930.000 \div 100 = 9300$ .
9,300
Write the number with 4 hundred-thousands, 7 thousands, 2 tens and 6 ones.
2 marks
Add $400.000 + 7000 + 20 + 6$ .
Keep zeros in the ten-thousands and hundreds positions.
407,026
Use each digit 0, 2, 4, 6, 7 and 9 once to make the greatest six-digit number.
2 marks
The highest place must receive the greatest remaining digit.
Arrange the digits from largest to smallest: 9, 7, 6, 4, 2, 0.
976,420

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum

Place value and powers of ten; efficient whole-number calculations and order of operations; factors, multiples and primes; prime factorisation and exponent notation; square numbers and square roots; estimation and rounding.

Official curriculum source ↗

In this lesson

Understand the idea.

Each position has a value

Powers of ten

See the method in action.

Explain a large number

Identify the occupied places.

Include the tens and ones.

Add the contributions.

Scale in two stages

Multiply the original number by 100.

Divide that result by 1,000.

Check the combined scaling.

Try it yourself.

Check your understanding

Keep practising