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eleminate proof needed tag
Now, looking at Wikipedia it seems this story is a rather simplistic summary of history, but then again my maths teacher was only using it to introduce us to the imaginary number system. Nonetheless it does show that imaginary numbers do actually exist, even if they may seem somewhat absurd to us. [[User:NormanS|NormanS]] 18:54, 23 August 2008 (EDT)
Now, looking at Wikipedia it seems this story is a rather simplistic summary of history, but then again my maths teacher was only using it to introduce us to the imaginary number system. Nonetheless it does show that imaginary numbers do actually exist, even if they may seem somewhat absurd to us. [[User:NormanS|NormanS]] 18:54, 23 August 2008 (EDT)
==Periodic Decimal Fractions are Ratios==
Just to eliminate this [proof needed]tag: <ul><li>Any decimal representation which repeats or recurs, like 1.86292929292929..., because these can be shown to be fractions[proof needed]</ul>
Now, here's an outline of the proof:
<ul><li>wlog, let 0 < x < 1 be a periodic decimal representation, i.e.,
<li><math> x = 0.\overline{a_1 a_2 ... a_n}</math>. Then
<li><math>x = \frac{a_1 a_2 ... a_n}{10^{n}-1} </math> as
<li><math>x =a_1 a_2 ... a_n \cdot 10^{-n}</math><math> + a_1 a_2 ... a_n \cdot 10^{-2n}</math><math> + a_1 a_2 ... a_n\cdot 10^{-3n} + ...</math> and
<li><math>10^{-n} + 10^{-2n} + 10^{-3n} + ... = \frac{10^{-n}}{1- 10^{-n}}</math></ul> --[[User:DirkE|DirkE]] 17:46, 25 August 2008 (EDT)