# 1 Big and small

The numbers that you encounter in everyday situations are usually of a reasonably manageable size, that is, they are generally not very big or very small. A person’s height may be 1.8 metres or the balance in a current account around a few hundred pounds. Both of these are numbers that are easy to understand and read. But what about the UK’s national debt? This is often quoted in billions of pounds, a number with at least ten digits! That is not quite so easy to write or understand when written down. Large numbers like this are often encountered in science and technology, as well as very small numbers. This is where scientific notation comes into its own.

One example of a very large distance is the width of the observable universe. This is about 92 billion light years, where a light year is about 9.5 trillion kilometres. A trillion is one thousand billion or a million million – which means a number followed by 12 zeroes. So to find the width of the universe in kilometres, you would need to multiply 92 billion by 9.5 trillion, since each light year is 9.5 trillion kilometres. How would you do that?

Well, you may want to use a calculator, but there’s a problem: 92 billion is 92 000 000 000, and that is too big a number for many calculators.

So how can you work this out? You could have worked the calculation out on paper, or multiplied 92 by 9.5 to get 874 and deduced that the distance must therefore be 874 billion trillion kilometres – or you may just have been bewildered by the enormity of the numbers! This is an example where scientific notation, which is based upon different powers of the number ten, could usefully be employed.

The next section will be a quick refresher on powers of ten, before moving onto how to use these in scientific notation. If you would like to refresh your knowledge of powers, take a look at *Succeed with maths – Part 1*. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]