*Our Maths specialist tutor explains some of the different types of numbers students need to know..*

**The natural numbers are**the maths of our everyday lives: there are two schools nearby; Cardiff has 358400 residents.

**The square numbers**are a subset of the natural numbers and are obtained by multiplying a number by itself. The first square number is 1 (since 1×1 = 1); the next is 4 (2×2) and the sequence continues with 9, 16, 25, 36 and so on. Taking the square root of a square number gets you back where you started, so √16 = 4 because 4×4 = 16. If you take the square root of a number that isn’t square (such as √2), you don’t get a whole number – the answer will be a decimal that goes on forever (√2 = 1.414123…)

**The negative numbers**are what you get if you subtract a larger number from a smaller one – take 7 from 5 say to leave minus 2.

**Rational numbers**can be written as a fraction; more formally, rational numbers can be written in the form p/q where p and q are both integers and q can’t be zero. Since q is allowed to be 1, all whole numbers can be written in this form and so are rational numbers. When rational numbers are written as decimals, the numbers after the decimal point either stop after a certain number of digits (e.g. 0.125 which is 1/8) or go on forever but follow a ‘pattern’ (e.g. 0.142857142857142857… which is 1/7).

**Irrational numbers**can’t be written in the form p/q. When written as a decimal, irrational numbers have no pattern after the decimal point and the digits go on forever. π is an example of an irrational number and while it’s commonly known as 3.142, the number of digits after the decimal point that we’ve calculated currently stands at around 1 trillion.

**Real numbers**include all the rational and irrational numbers.

**Juliet Ash is a Cardiff & Vale tutor of A level Pure Maths and Physics. Contact us at Cardiff & vale tutors if you need help with Maths Tuition.**