Thread: fractions

given a fraction n/d you can effectively do long division like this:

Code:

  value in before decimal = n/d (integer arithmetic)
  remainder before decimal = n % d;
  1st value after decimal = (10 * remainder before decimal) / d
  1st remainder after decimal = (10 * remainder before decimal) % d
  2nd value after decimal = (10 * 1st remainder after decimal) / d
  2nd remainder after decimal = (10 * 1st remainder after decimal) % d
  ... and so on until either:
    the remainder is 0 - no repeating necessary
  or:
    you repeat a previous remainder - decimal notation has a repetition

The code to do this is actually not as complex as I at first thought
- its an interesting problem )

Originally Posted by DavT

given a fraction n/d you can effectively do long division like this:

Code:

  value in before decimal = n/d (integer arithmetic)
  remainder before decimal = n % d;
  1st value after decimal = (10 * remainder before decimal) / d
  1st remainder after decimal = (10 * remainder before decimal) % d
  2nd value after decimal = (10 * 1st remainder after decimal) / d
  2nd remainder after decimal = (10 * 1st remainder after decimal) % d
  ... and so on until either:
    the remainder is 0 - no repeating necessary
  or:
    you repeat a previous remainder - decimal notation has a repetition

The code to do this is actually not as complex as I at first thought
- its an interesting problem )

That's the ticket! Use custom decimal arithmetic routines for dividing decimal numbers with an arbitrarily large number of digits.

My thoughts were that if you put the digits as '0' and '1' into an ascii string, then you could use strstr() or some such thing to test for periodicity.

(Maybe a good exercise for you recursion geeks.)

After you have identified a candidate, then use some method like the one in the first post by okinrus to recreate the original fraction (assuming that common factors have been removed so that the numerator and denominator are relatively prime). You could do this arithmetic in decimal also, using a custom multiplication and subtraction routines.

My only problem is knowing how to stop (not how to stop the program, but how to stop thinking of ways to do it, given the good ideas presented by the good people here).

Regards,

Dave