Question

Express 32.1235(bar on 35) in the form of p/q

Answer 1

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Answer 2

Answer:

The expression $32.12 \overline { 35 }$ in the form of p/q is $\frac {318023}{9990}$

Solution:

Let

$\begin{array} { l } { x = 32.12 \overline { 35 } } \\\\ { = 32.123535353535 \ldots } \end{array}$

Any number which has a bar on its head tends to be repeating infinite times.

Here, 35 is repeating continuously

Let us take

$\begin{aligned} 10000 x & = 10000 \times 32.12353535 \ldots \\\\ & = 321235.353535 \ldots \\\\ 100 x & = 100 \times 32.12353535 \ldots \\\\ & = 3212.353535 \ldots \end{aligned}$

Subtracting 100x from 10000x, we get

$\begin{array} { c } { 10000 x - 100 x = 321235.353535 \ldots - 3212.353535 \ldots } \\\\ { 9900 x = 321235 - 3212 = 318023 } \\\\ { x = \frac { 318023 } { 9900 } } \end{array}$

Thus the value of x in terms of p/q is given as,

$\begin{aligned} x & = \frac { 318023 } { 9990 } \\\\ \frac { p } { q } & = \frac { 318023 } { 9990 } \end{aligned}$