Question

Express in p/q form -5.2 bar

Answer 1

let x = 5.2bar, 10x = 52.2bar, 10x-x= 47, 9x = 47, x = 47/9

Answer 2

Answer:

The value of $5 . \overline { 2 }$ in p/q form is 47/9

Solution:

Given number

$x = 5 . \overline { 2 } = 5.222222 \ldots$

Multiplying x by 10, we get,

$\begin{aligned} 10 x & = 5.222 \ldots \times 10 \\\\ = & 5.2222 \ldots \times 10 \\\\ & = 52.2222 \ldots \end{aligned}$

Multiplying x by 1 we get,

$\begin{aligned} 1 x & = 5.222 \ldots \times 1 \\\\ & = 5.2222 \ldots \end{aligned}$

Subtracting the term 1x from 10x, we get,

$\begin{array} { c } { 10 x - 1 x = 52.2222 \ldots . - 5.2222 \ldots \ldots } \\\\ { 9 x = 52.000 - 5.000 } \\\\ { 9 x = 47 } \\\\ { x = \frac { 47 } { 5 } } \end{array}$

Then, the p/q form of the $5 . \overline { 2 }$  is 47/9.

Hence, $5 . \overline { 2 } = \frac { 47 } { 9 }$