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Numbers, units and arithmetic
Numbers, units and arithmetic

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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.


Millions Hundred Thousands Ten Thousands Thousands Hundreds Tens Units
2 0 0 0 0 0 0
2 2 0 1 9 9 5

Now look at the numbers from the left. Both numbers have a 2 in the millions column, so move to the next place. The first number has a 0 in the next column (i.e. hundred thousands) whereas the second number has a 2. So the second number is larger, the announcement was correct and more than two million pounds was paid out.

In practice you probably won’t want to write the headings in the columns each time. But do keep their meanings in mind.