In base ten, $(0.\overline{10}) =\frac{10}{99}$ .

What about in base three?

What is $(0.\overline{10})_3$ ?

Give your answer to 3 decimal places in base 10.

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Notation:
**

- $0.\overline{10} = 0.10101010101010\ldots$ .
- The subscripts indicate the base.

The answer is 0.375.

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Here are two ways to approach this one:

1) $(0.101010...)_3 = \frac{1}{3^1} + \frac{1}{3^3} + \frac{1}{3^5} + ... = \frac{3}{8} = \boxed{0.375}$

2) Let $x = (0.101010...)_3$