Where are all the acids?

Number Theory Level 4

$A=2.\overline2_5$

Convert $A$ to base $10$ . Round your answer to three decimal places.

Clarification : The subscript means number base $5$ . The line over the $2$ represents an infinitely repeating decimal.

Inspired by my girlfriend

1 solution

Alex G
May 1, 2016

$2.\overline2_5 = 2 + 2 \cdot 5^{-1} + 2 \cdot 5^{-2} + ....$

$\sum_{n=0}^{\infty} \dfrac{2}{5^n}$

$\dfrac{2}{1-\frac{1}{5}}$

$\dfrac{5 \cdot 2}{4}$

$2.5$

You'll need to correct the question, You've got 0.222222222... what you mean is 2.22222222 Good problem though

William Whitehouse - 5 years, 1 month ago

Thanks alot! Sorry about that

Alex G - 5 years, 1 month ago