Question

Best to use an example to describe the problem. Lets say I have a decimal value 100.227273.

100.227273 * X = Y

I need to find the smallest positive integer X that gives integer Y.

Answer 1

If the 100.227273 is just an approximation and you want to get the best rational approximation, use continued fractions.

Take 100.227273 as example.

1. Take the integer part (100) away. Now you get 100.227273 = 100 + 0.227273.
2. Invert 0.227273 to get 4.39999 (4.4?).
3. Repeat step 1 until you are satisfied with the error.

So you get

                       1
100.227273 = 100 + —————————
                         1
                   4 + —————
                           1
                       2 + —
                           2

Simplify this expression to get 2205/22.

[Editor’s note: For example code, see this answer.]