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

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- Jun 3rd 2008, 01:18 AMStevo_Evo_22Applications of infinite geometric series
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 - Jun 3rd 2008, 02:04 AMbobak
Hello Stevo

I would first write

$\displaystyle 0.454545454545 \cdots$

as

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

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

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

Bobak