Why do I get a repeating decimal when I divide?

Answer 1

When you get a repeating decimal when dividing, it means that the decimal representation of the quotient has a repeating pattern of digits. This occurs when the divisor (the number you're dividing by) is not a factor of 10, leading to a situation where the division process does not result in a clean, terminating decimal. The repeating decimal is a way to represent the fraction that results from the division in a concise form.

Answer 2

Any TERMINATING decimal can be written as a fraction with a denominator that is a power of 10 - which has the prime factors 2 and 5. Therefore, any fraction (in simplest terms) must have a denominator which is only made up of the prime factors 2 and 5. Any other factor, and the fraction will not be terminating.As to why it repeats, that's because in the division, there are only so many options. For example, if you divide by 7, the remainder, in each step of the division, can only be a number between 1 and 6. Eventually, the pattern will repeat.

Answer 3

You will get a repeating decimal (or decimals) if the divisor, in the simplified form of the division, contains any prime factor other than 2 or 5.