Radix Conversions

Question

I've just managed to Number.prototype.toString(radix) also with floating point numbers. Regular Integers are converted to Strings this way:

var rest = Math.floor(this.valueOf());  // ignoring the -/+ in this example
var result = '';

while(rest >= radix)
{
    result = alphabet[rest % radix] + result;
    rest = Math.floor(rest / radix);
}

if(rest >= 1) result = alphabet[rest] + result;

Now I've appended this for possible floating points:

var rest = this.valueOf() % 1;
var zeros = 0;

if(rest === 0) return result;
else while(rest % 1 !== 0)  // => "is float?"
{
    rest *= radix;
    // leaving out the initial 0 count, as counted in the variable 'zeros'
}

result += '.' + String.repeat(zeros, alphabet[0]) + rest.toString(radix);

But my result strings for floating points are too large see this example screenshot. So, what is/are the additional while() statement(s)? My regular code is here: from line 314 and below.

MAYBE there's a way to handle the floating points in parallel to and within the first (int-)while() [so one side /=, the other *=, or smth. similar]?

Thank you.