For anyone wondering how to do this faster (without converting to string), here’s a solution:
function precision(a) {
var e = 1;
while (Math.round(a * e) / e !== a) e *= 10;
return Math.log(e) / Math.LN10;
}
Edit: a more complete solution with edge cases covered:
function precision(a) {
if (!isFinite(a)) return 0;
var e = 1, p = 0;
while (Math.round(a * e) / e !== a) { e *= 10; p++; }
return p;
}