Converting float decimal to fraction

Question

I am trying to convert calculations keyed in by users with decimal results into fractions. For e.g.; 66.6666666667 into 66 2/3. Any pointers? Thanx in advance

Answer 1

Continued fractions can be used to find rational approximations to real numbers that are "best" in a strict sense. Here's a PHP function that finds a rational approximation to a given (positive) floating point number with a relative error less than $tolerance:

 $n*$tolerance);

    return "$h1/$k1";
}

printf("%s\n", float2rat(66.66667)); # 200/3
printf("%s\n", float2rat(sqrt(2)));  # 1393/985
printf("%s\n", float2rat(0.43212));  # 748/1731

I have written more about this algorithm and why it works, and even a JavaScript demo here: https://web.archive.org/web/20180731235708/http://jonisalonen.com/2012/converting-decimal-numbers-to-ratios/