Asked by ABC123

Express $0.\overline{21}_3$ as a base 10 fraction in reduced form.
Answered by oobleck
0.21... = 21/99
I'm sure you can reduce that as needed
Not sure what the _3 contributes ...
Answered by oobleck
or was that 0.21... a base-3 number?
Well, that would of course be 21/22<sub><sub>3</sub></sub> = 7/8<sub><sub>10</sub></sub>
Answered by hello
no its 7/8
Answered by lexi
its 7/8 !
Answered by Guest
To get the answer quickly we can use a geometric series .21212121... = 7/9+7/81+7/729..., = 7/8

A more simply but longer method is to make .21212121..._3 equal to X, and then multiply both sides of the equation by 100_3. This makes 100_3*X=21.212121..._3, so 100_3*X=21+X, because 0.212121..._3 = X. Then, we have 22_3X=21_3, after subtracting one equation from the other. So, X= (21_3)/(22_3). In base 10, this is (2*3+1)/(2*3+2)= 7/8

*Note that number_3 is that number is base 3
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