It is very straight forward to figure out from the binary representation. The floats have 23 bits (and the implied most significant bit is 1), while doubles have 52 bits (and the implied most significant bit is 1). It is something like 7 and 15 decimal places, approximately.
Keep in mind that round off errors can accumulate with complex and multiple calculations. In the end, you may not have this accuracy, despite the precision of the representation.