## Welcome to H3 Maths

Blog Support for Growing Mathematicians

### Why don’t tape measures show √2?

March3

Your boss asks you to cut a length of wood exactly to √2. So, you get out your tape measure and ….what? There is NO √2! There should be though? After all, √2 is an exact length!! It was worked out on a calculator so you should be able to measure it? Why don’t rulers and tape measures show √2, just like our calculators?

The problem, you see, is that √2 is an irrational number. In other words, it never occupies an exact place on a ruler or tape measure. Irrational numbers, like √2 and pi, have infinite, non-recurring, decimal expansions. Therefore, it is only as accurate as you need it to be. For example, √2 = 1.4 which might, for example, be a distance in kms. 1.4km = 1400m. But √2 also = 1.41 which is 1410m and so on. You set the expansion of √2 to suit what you are measuring. That is why you don’t find √2 on your ruler! √2 is also a great reason to think about abstract ideas in Mathematics, which is a bit like an Alice in Wonderland for numbers!

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