Why is a base 10 decimal "fraction" okay but a non base 10 fraction not okay?

Annie French

Annie French

Answered question

2022-11-14

Why is a base 10 decimal "fraction" okay but a non base 10 fraction not okay?

Answer & Explanation

Kennedy Evans

Kennedy Evans

Beginner2022-11-15Added 16 answers

Any base- n-fraction p q will continue WITH a pattern, repeating with a length of at most q 1 repeating digits where q is its denominator - no matter what base you are looking at.
For example, while 1 7 = 0. 142857 ¯ 10 = 0.1 7 , 1 10 = 0.1 10 = 0. 0462 ¯ 7
If a number repeats or stops in base 10, it will continue or stop in any other base n as well.
On the other hand, irrational numbers are those where you cannot find any repetitions in the digits in any base.

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