question_answer

Find the prime factorisation of the denominator of rational number expressed as \[6.\overline{12}\] in simplest form.

Answer:

Let \[x=6.\overline{12}\]                                    ?(i)

\[\Rightarrow 100x=6.\overline{12}\]                                      ?(ii)

Subtracting eq. (i) from (ii), we get

\[99x=606\]

\[x=\frac{606}{99}=\frac{202}{33}\]

\[\therefore \]      Denominator \[=33\]

Prime factorisation \[=3\times 11\]