document.write( "Question 833306: What fraction is represented by 0.17952? where the 952 is repeating. \n" ); document.write( "

Algebra.Com's Answer #502465 by KMST(5328) $\"\"$ $\"About$

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So 17.952952952.... = $\"17%26952%2F990\"$
\n" ); document.write( "Similarly,if $\"x=0.17952952952\"$ $\"%22...%22\"$
\n" ); document.write( " $\"1000x=179.52952952952\"$ $\"%22...%22\"$
\n" ); document.write( "Then,
\n" ); document.write( " $\"1000x-x=179.52-0.17\"$ (the rest of the digits cancel out)
\n" ); document.write( " $\"999x=179.35\"$
\n" ); document.write( " $\"99900x=17935\"$
\n" ); document.write( " $\"x=17935%2F99900\"$
\n" ); document.write( "Can we simplify that fraction?
\n" ); document.write( "

\n" ); document.write( " $\"17935\"$ is not divisible by $\"2\"$ or by $\"3\"$ , but we can divide it by $\"5\"$
\n" ); document.write( " $\"17935%2F5=3587\"$ and $\"99900%2F5=19980\"$ so
\n" ); document.write( " $\"17935%2F99900=3587%2F19980\"$
\n" ); document.write( " $\"3587\"$ is not divisible by $\"5\"$ or $\"37\"$ so we cannot simplify the fraction further.
\n" ); document.write( " $\"x=highlight%283587%2F19980%29\"$ \n" ); document.write( "

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