Fractional/rational form of 0.999... Is it possible to express 0.999..., a repeating number, as a fraction? Or as a ratio of two numbers? Basically all (my) attempts at the problem cancels all the terms and returns 1. Is it even possible? Or has it been proven to be an exercise of futility?

Kaylynn Cook

Kaylynn Cook

Answered question

2022-11-12

Fractional/rational form of 0.999...
Is it possible to express 0.999..., a repeating number, as a fraction? Or as a ratio of two numbers?
Basically all (my) attempts at the problem cancels all the terms and returns 1. Is it even possible? Or has it been proven to be an exercise of futility?

Answer & Explanation

Haylie Park

Haylie Park

Beginner2022-11-13Added 14 answers

Yes, it can: 0.999999999999 = 1 1
assupecoitteem81

assupecoitteem81

Beginner2022-11-14Added 3 answers

Let
x = 0.99999 ,
now
10 x = 9.99999 ,
then
10 x x = 9 x = 9 x = 1.

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