Question

Express 5.12bar in the form of p/q

Answer 1

$\underline{\mathfrak{\huge{The\:Question:}}}$

Express $\tt{5.\overline{12}}$ in the form of $\tt{\frac{p}{q}}$

$\underline{\mathfrak{\huge{Here's \:Your\:Answer:}}}$

Let :

$\tt{5.\overline{12} = x}$ [ Let this be equation (1) ]

Multiply this formed equation by 100 ( × 100 )

$\tt{5.\overline{12} \times 100 = x \times 100}$

Solve this equation further

$\tt{512.\overline{12} = 100x}$ [ Let this be equation (2) ]

Now, subtract equation (1) from equation (2) :

$\tt{512.\overline{12} - 5.\overline{12} = 100x - x}$

Solve this formed equation further

$\tt{507 = 99x}$

Take 99 on the other hand side and then find the value of x by solving the formed equation further

$\tt{x = \frac{507}{99}}$

There you got the value of $\tt{5.\overline{12}}$.