N1NumberFoundation

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.

20 min AQA GCSE Maths

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.

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

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.

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

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