Dividing by 41

[ll_billym]

I had to divide a few numbers by 41 recently (because it is the GBP/CZK exchange rate), anyway the answers all ended with a repeating pattern:

215 = 5.2439024390243902439024390243902

5748 = 140.19512195121951219512195121951

666 = 16.24390243902439024390243902439

3499 = 85.341463414634146341463414634146

In fact any number I could find (apart from multiples of 41) divided by 41 gives this kind of pattern.

I thought it might be because it's a prime number but dividing by other primes I tried doesn't give that result.

Is there a mathematical reason why this particular number always gives this type of result?

Thanks.

[scotstone]

If you divide by 41 and there is a remainder then you will have a fraction x/41. As 1/41 is a repeating decimal ie .02439024390.... then if x is any number except multiples of 41 then the answer will be x * 1/41 which will automatically be a repeating decimal. This works for other prime number denominators except 2 and 5 which are factors of 10 and denominators which can be expressed as two numbers one of which (or both) is a prime number (except 2 and 5). Obviously the numerator is not to be a multiple or submultiple of the denominator. This can be checked on a calculator but some of the repeats may extend beyond the decimal places of the calculator.

[ll_billym]

Nice one, very well explained.