Question

when writing a repeating decimal as a fraction, why does the fraction always have only 9s or 9s and 0s as digits in the denominator

Answer 1

thats not necessarily true. 0.8333... is just 5/6 as a decimal. I suppose it depends on the number.

Answer 2

When writing a repeating decimal as a fraction the denominators are not always only 9s or 9s and 0s

The repeating decimal is as a result of the numbers ( i.e. the numerator and denominator values ) and not necessarily because the digits in the denominator are only 9s or 9s and 0s.  as seen in the example below.

Example :  5/6  and 5/3 expressed as a decimal

5/6 = 0.83333333

5/3 = 1.66666---

Hence the repeating decimal as a fraction in number is dependent on the values of the numerator and denominator and not on 9s or 9s and 0s

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