1MA1 · N1–N2NumberFoundation

Place Value & Ordering

Every digit in a number has a value that depends on its position — this is called place value. Once you understand it, you can read, write and order any whole number or decimal with confidence.

35 min Pearson Edexcel GCSE Maths (1MA1)

The big picture

Place value is the structure behind almost every numerical method in GCSE Maths. It explains why multiplying by 10 moves every digit one column, why decimal points must line up, and why a number written in standard form has the size it does.

Edexcel questions rarely ask only for a definition. They place positive numbers, negatives, decimals and fractions together, then test whether you can compare or order them without being distracted by their different forms.

What you'll learn

Know the value of each digit in a number
Write numbers in words and figures
Order whole numbers and decimals by size
Use the < and > symbols correctly

What place value means

In the number $3452$ , the $3$ is worth three thousand, the $4$ is four hundred, the $5$ is fifty and the $2$ is just two. The same digit is worth ten times more each time it moves one place to the left.

After the decimal point the columns keep getting ten times smaller: tenths, then hundredths, then thousandths.

Why this works

A digit has no fixed value on its own: its column supplies the scale. The 7 in 7.2 means seven units, while the 7 in 0.072 means seven hundredths.

Tip — Line numbers up by their decimal point — it keeps each digit in the right column.

Ordering numbers

To put numbers in order, compare the biggest place-value columns first. The symbol $<$ means “less than” and $>$ means “greater than”. The arrow always points to the smaller number.

1Compare the tenths column first:

0.07

has

0

tenths, the others have

7

2So

0.07

is smallest.

3Then compare

0.7

and

0.77

in the hundredths column.

Answer

0.07 < 0.7 < 0.77

Why this works

A reliable comparison uses a common form. Write decimals with the same number of decimal places, or convert fractions and decimals before ordering them.

Think like an examiner

When ordering values, write the complete ordered list in your final line. Working alone may not earn the answer mark.
For negative numbers, the value farther left on a number line is smaller: $- 8 < - 3$ , even though 8 is the larger magnitude.
Keep trailing zeros while comparing decimals: writing $0.7$ as $0.700$ makes its place-value relationship to $0.67$ immediately visible.

Remember these

a < b

“a is less than b” — arrow points to the smaller value.

a > b

“a is greater than b”.

Watch out for these

Thinking

0.45

is bigger than

0.5

because it has more digits.

Compare column by column:

0.5

has 5 tenths,

0.45

has only 4 tenths, so

0.5

is bigger.

Mixing up the

<

and

>

symbols.

The pointy end always points at the smaller number.

Stretch yourself

Use each digit 1, 3, 5 and 7 exactly once to make the greatest number smaller than $4$ , then make the smallest positive number greater than $0.1$ .

Hint — The position of the decimal point controls the size before the remaining digits fine-tune it.

Questions students ask

Why does multiplying a decimal by 10 not mean “add a zero”?

Each digit becomes ten times as valuable, so it moves one place to the left relative to the decimal point. Adding a zero fails for numbers such as

2.7

0.40

larger than

0.4

No. A trailing zero after the final decimal digit does not change the value, so

0.40 = 0.4

Key takeaways

Each digit’s value depends on its column (place value).
Compare the biggest columns first when ordering.
$<$ means less than, $>$ means greater than.

Test yourself

Ready to practise Place Value & Ordering? Pick a mode and earn XP & Dobloons.

Next step

Practise this topic

Real past-paper questions on Place Value & Ordering, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.

Practise this topic