Place value and powers of ten | Year 7

01 / LEARN

The idea, step by step

Each position has a value

Our base-ten system groups ten of one unit into one of the next unit. In 4,072,305, the 7 represents seven ten-thousands, not seven thousands. A zero holds a position where there are no units of that size.

Expanded form shows the non-zero parts of a number. Read the place first, then multiply the digit by that place value.

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

Powers of ten

The notation $10^{3}$ means $10 \times 10 \times 10 = 1000$ . Multiplying by 1,000 makes every digit worth 1,000 times as much; dividing by 1,000 makes every digit worth one-thousandth as much.

Write the result using the place values, rather than attaching or deleting zeros without thinking. For example, $46.000 \div 1000 = 46$ because 46 thousands are being regrouped into units.

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

A common trap

The digit 7 always has a value of 7.

Instead: A digit has a face value and a place value. In 70,000, the 7 contributes 70,000.

02 / WORKED EXAMPLES

See the thinking

Example 1

Explain a large number

Write 5,308,042 in expanded form.

The digits represent 5 millions, 3 hundred-thousands, 8 thousands, 4 tens and 2 ones.
The zero digits contribute no extra amount.
Add the non-zero place-value parts.

5.000.000 + 300.000 + 8.000 + 40 + 2

Example 2

Scale in two stages

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

Multiplying by 100 moves each digit to a place worth 100 times as much: $3640 \times 100 = 364.000$ .
Dividing by 1,000 gives $364.000 \div 1000 = 364$ .
The combined scaling is multiplication by one tenth.

364

Check your understanding

What does the 8 represent in 583,214?

Show answer

80,000

The 8 is in the ten-thousands position, so its contribution is $8 \times 10.000$ .

03 / WORKSHEET

Your turn

6 questions · 12 marks · Work at your own pace.

Worksheet PDF 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 ↗

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