Applications of infinite geometric series

**Stevo_Evo_22** · June 3rd 2008, 01:18 AM

Hi all,

Just a quick question which I'm stuck on, having never done one before....

Express in the form a/b: 0.45 (so that both the 4 and 5 are recurring)--0.4444444.......55555555..........

Thanks in advance!
Steven

**bobak** · June 3rd 2008, 02:04 AM

Originally Posted by Stevo_Evo_22

Express $0.454545454545 \cdots$ as a fraction in the form $\frac{a}{b}$ where $a$ and $b$ are integers.

Hello Stevo

I would first write

$0.454545454545 \cdots$

as

$45 \times 10^{-2} \ + \ 45 \times 10^{-4} \ + \ 45 \times 10^{-6} \ + \ 45 \times 10^{-8} \cdots$

$\Rightarrow 45 ( 10^{-2} \ + \ 10^{-4} \ + \ 10^{-6} \ + \ 10^{-8} \cdots )$

Just find the sum of the infinite geometric series and simplify.

Bobak

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