We’ve covered quite a lot already on the numbers, how to use mental arithmetic to make maths easier, and lastly how factors of a number help further with calculations including working out the largest number two numbers can be divided by (highest common factor: HCF) and the smallest number that both numbers can divide into (lowest common multiple: LCM) – Hint: the HCF is a small number and the LCM is a big number, at least big as the biggest number). All of this gives us a good set of tools and tricks to manage numbers better.

Now, we are going to take our first step away into non-conventional numbers and maths. Not too far but certainly a view that is only used by most people that need to use maths not purely for counting and measuring but into using maths as a way of modelling the universe around us. This sounds intimating so I’ll take it nice and slow for my sake and hopefully for yours.

All numbers have a base and an index

Think of any number (to be more specific I mean any integer just in case you were trying to be clever) say 7 but whatever number you have thought of is just as good.

7

This number is a symbol that represents 7 things. These things can be physical things like 7 balls. Or it could be part of an instruction to do something to another number like multiply 2 by 7 to get 14. All good. Nothing new here. But there is more to this number than meets the eye. We can add information to this number to describe it even more.

Every number has two describes one that you can see and one you often not as its not helpful information. The first is the number itself is called the base. The reason it’s called the base as this is where we start from. The other thing you can’t see is the index. The reason you can’t see it is because it’s not there but all numbers have an index and if not written down then the index is 1. So we can write 7¹ but we don’t we just write 7.

What is an index of a number?

An index or power or exponent of a number is a description of how many times big or small that number is than the base – how much it grows.

For example 2 x 2 is 4 or 2 squared. We write squared with an index of 2 so 2 x 2 is the same as 2² or take the number 2 (the base) and double it/grow it by a factor of 2. If we can change the base to say 13 and square it then we are saying grow it (multiple it) by it factor of it self – 13 x 13 = 169 = 13². Note – we are not doubling a number when we square it – that only works for when the base is 2.