For example, denominators of 0.1 (1 / 10) and 0.2 (1 / 5) are not powers of two, so these numbers can’t be finitely represented in a binary format.
Only fractions with a denominator which is a power of two can be finitely represented in a binary form. So, 0.375 in decimal system is represented as 0.011 in binary. Now, let’s just write out the resulting integer part at each step - 0.011. Here is an example of such conversion using the fraction 0.375. Then just write out the integer parts from the results of each multiplication. Continue multiplying by 2 until you get a resulting fractional part equal to zero. To convert fraction to binary, start with the fraction in question and multiply it by 2 keeping notice of the resulting integer and fractional part.
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