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Decimal Fractions

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A rational number $ p/q$ can be written as a finite decimal fraction

$\displaystyle \frac{p}{q} = a_1\cdots a_m.b_1\cdots b_n\, , $

if and only if the denominator $ q$ contains only $ 2$ and $ 5$ as prime factors.

If $ q$ contains other prime factors as well, then $ p/q$ can be written as an infinite periodical decimal fraction:

$\displaystyle \frac{p}{q} = a_1\cdots a_m.b_1\cdots b_n\overline{c_1\cdots c_k} \,, $

where the sequence $ c_1\cdots c_k$ repeats itself infinitely often.

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  automatisch erstellt am 19.  8. 2013