How do I find infinitely long decimals in an array

So I made an array that contains fractions (1/2, 1/3, 2/3, etc) and what I have set up is that the user types in two numbers, the program divides them and subtracts until it's left with only the decimal point, and saves that as a global variable, then the program tries to find a corresponding fractions but I'm encountering rounding issues

For example if the user types in 100/6 the answer is 0.666666668 but in the array 1/3 is 0.6666666666

So the program doesn't work because these are two different values because it was round. Is there any way around this?

I would suggest just going to the hundreds, or thousands decimal place.

mid(), left()

Then int(), back to numbers.

There is always going to be rounding, so finding an exact decimal number in the array may not work. Usually when comparing decimal or floating point numbers you'd do abs(num1-num2)<0.0001 or some sufficiently small number.

You may be able to get by if you reduce the number before dividing. So maybe (num1%num2)/num2

A full solution is to reduce the fraction first before dividing so that 1/3 and 10/3 with the numbers before the decimal will be identical.

Num1=num1%num2

g=gcm(num1, num2)

Result=(num1/g)/(num2/g)

Gcm is the greatest common multiple. You could look at Wikipedia to see how to do that.