Become an OU student

Numbers, units and arithmetic

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

1.1 Whole numbers

Whole numbers arise from counting: for example the number of sheep in a field or the number of votes in an election.

Our everyday number system is the decimal system, where the position of a digit within the number determines whether it represents units, tens, hundreds, thousands etc.

For example, the number 1375 means one thousand three hundred and seventy-five. The position of the 3, third from the right, means that it represents 3 hundreds.

A thousand thousand, 1 000 000, is called a million and a thousand million, 1 000 000 000, is called a billion. (A British billion used to be a million million, but now the US convention of a thousand million is normally used.) To compare two numbers, it sometimes helps to write them, or think of them, in columns:

 Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Units

The position of a digit in the columns is called its place value.

Example 1

A lottery organiser announces that this week’s winnings will be over two million pounds. After the draw, the organisers announce that the winnings were £2 201 995. Was the announcement correct?

The issue is whether the figures represent a number greater than two million, or not. Write the two numbers in a number column table. Start with two million.