Decimal numbering: classes, ranks and the value of digits

The decimal system

Our number system is base 10: we use ten digits (0 to 9) and the position of a digit within a number determines its value. This is known as ‘place value’ or ‘rank’.

Example: in the number 4 523:

• the digit 3 is in the ones place -> it is worth 3
• the digit 2 is in the tens place -> it is worth 2 × 10 = 20
• the digit 5 is in the hundreds place -> it is worth 5 × 100 = 500
• the digit 4 is in the thousands place -> it is worth 4 × 1,000 = 4,000

Place value groups

To read a large number easily, it is broken down into groups of three digits, starting from the right: ones, thousands, millions, billions.

Billions	Millions	Thousands	Ones
2	305	018	764

This table is read as: two billion three hundred and five million eighteen thousand seven hundred and sixty-four.

Method

1. Break the number down into groups of three digits starting from the right (leave a space, never a full stop).
2. Label each group starting from the left: billions, millions, thousands, units.
3. Read each group as a three-digit number.

Common pitfall

Never use a full stop to separate the thousands in French (1.000 is incorrect): use a space, as in 1 000. The full stop is used in other countries and could be mistaken for a decimal point.

Another common mistake: omitting a ‘silent’ zero in a place value, for example writing 5 007 instead of 5 070 for ‘five thousand and seventy’ – every place counts, even when the digit is 0.