Each place in a decimal number represents a power of ten. Before the decimal point we go from ones to tens, to hundreds, to thousands, etc. After the decimal point we go to tenths, hundredths, thousandths, etc.
When the number changes the principle is the same. On the left of the point we start at the ones just as in decimal, but as we move leftwards through the digits we multiply by the base so that we have increasing powers of the base.
On the right of the point we have the reciprocal of the same powers of the base (progressively negative powers of the base). For example, if the base is 2, we can only have the digits 0 or 1 in the number, whether it's before the point or after it; in base 3, only the digits 0, 1 and 2 can be used. So the digits anywhere in the number must always be 0 up to one less than the base. Base 2 numbers are usually called binary numbers. Here's how we count in binary: 1, 10, 11, 100, 101, 110, 111, 1000 (decimal 1-8). Each progressive digit represents a progressive power of 2. 101 represents 22+1=5, for example.
In base 3 (ternary system) the decimal number 5 would be 31+2 which looks like 12.
Binary fractions can still be represented in the form a/b where a and b are binary numbers. But when we use the period or full-stop (.) to separate the integer part from the fraction part, 0.1 would represent a half (1/10 in binary); 0.01 would represent a quarter (1/100); three-quarters would be 11/100=0.11, and so on. In all number systems the principle is the same--progressive powers of the base (including the negative powers: 1/2=2-1, 1/4=2-2, 1/8=2-3, etc., for binary numbers).
The base 2 number (binary) 0.001 is ⅛ decimal, being the third binary place after the point.