In the fraction 1&#x2F;10, the denominator is 10.
The prime factors of 10 are 2 and 5.<p>Binary does not contain the prime factor of 5 necessary to represent 1&#x2F;10 cleanly as a decimal. It only contains the 2.<p>Similarly, the prime factors for 1&#x2F;6 would be 3 and 2. In a base 10 number system, you only have the 2. So you end up with a repeating decimal (0.1666666).