Place Value & Ordering

Spec reference: Number - Structure and calculation
Key idea: Understand the value of each digit in a number and use this to order and compare numbers.

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Place value

Every digit in a number has a place value depending on its position.

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Units	.	Tenths	Hundredths	Thousandths
1,000,000	100,000	10,000	1,000	100	10	1	.	0.1	0.01	0.001

Example

In the number 3,472.56:

• 3 is in the thousands column - it represents 3,000
• 4 is in the hundreds column - it represents 400
• 7 is in the tens column - it represents 70
• 2 is in the units column - it represents 2
• 5 is in the tenths column - it represents 0.5
• 6 is in the hundredths column - it represents 0.06

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Ordering numbers

To order numbers, compare digit by digit from left to right.

Example

Order these numbers from smallest to largest: 3,412, 3,142, 3,421, 3,124

Line up the digits:

Thousands	Hundreds	Tens	Units
3	1	2	4
3	1	4	2
3	4	1	2
3	4	2	1

All have the same thousands digit (3), so compare hundreds: 1 < 4.

Comparing the two with hundreds digit 1: 3,124 < 3,142

Comparing the two with hundreds digit 4: 3,412 < 3,421

Answer: 3,124 ; 3,142 ; 3,412 ; 3,421

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Ordering decimals

Common mistake

Do not compare decimals as if they were whole numbers.

$0.35>0.8$ is wrong - pad with zeros: $0.35$ vs $0.80$, so $0.35<0.80$

Always line up the decimal points, then compare digit by digit.

Example

Order from smallest to largest: 0.3, 0.35, 0.305, 0.03

Units	.	Tenths	Hundredths	Thousandths
0	.	3	0	0
0	.	3	5	0
0	.	3	0	5
0	.	0	3	0

Answer: 0.03 ; 0.3 ; 0.305 ; 0.35

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Multiplying and dividing by powers of 10

Operation	Effect on digits
$\times 10$	Move all digits 1 place left
$\times 100$	Move all digits 2 places left
$\times 1000$	Move all digits 3 places left
$÷10$	Move all digits 1 place right
$÷100$	Move all digits 2 places right
$÷1000$	Move all digits 3 places right

Examples

• $4.7\times 100=470$
• $3500÷1000=3.5$
• $0.06\times 1000=60$

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Negative numbers

Negative numbers are less than zero. On a number line, they appear to the left of 0.

$$\dots -4,-3,-2,-1,0,1,2,3,4\dots$$

Ordering negatives

Order from smallest to largest: -3, 5, -7, 2, -1

On a number line, further left = smaller.

Answer: -7, -3, -1, 2, 5

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Exam tips

Watch out for

• Confusing place value in decimals - always line up the decimal point
• Saying $-7>-3$ because 7 > 3 - the opposite is true for negatives
• Not padding decimals with zeros when comparing (e.g. comparing 0.3 and 0.35)

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Test Yourself

Question 1 of 5

What is the value of the digit 7 in 3,742?