What is an integer?

Natural numbers

A natural number is used to count objects: 0, 1, 2, 3, 4, 5… and so on to infinity. This set is often denoted by the letter N (the set of natural numbers).

These numbers have no decimal point and are never negative. They are used to count: the number of pupils in a class, the number of apples in a basket, the current year…

Digits and numbers: don’t confuse them

A digit is one of the following ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A number is a sequence of digits that represents a quantity.

Example: the number 305 is written using three digits (3, 0 and 5), but it is a single number: three hundred and five.

Examples

Number	Spelling
7	seven
42	forty-two
1000	one thousand
25 604	twenty-five thousand six hundred and four

Common pitfall

Do not confuse ‘digit’ with ‘number’: saying ‘1,000 has four digits’ is correct, but saying ‘1,000 is a digit’ is incorrect, as 1,000 is a number made up of four digits.

Another pitfall: 0 is indeed a natural number (it is the smallest one), but it is not counted amongst the ‘strictly positive’ numbers used later in Year 7 – simply remember that it belongs to N.

These concepts form the basis of all arithmetic: without clearly distinguishing between digits and numbers, you risk making mistakes as early as secondary school when reading and writing large numbers.