Question

Express 0.18 bar in form of p/q

Answer 1

LET X BE 0.1818..

THEREFORE,100*X

=100*0.1818=18.1818....

100X=18+X

100X-X=18

99X=18

X=18/99

Answer 2

$\displaystyle \bf{ 0. \overline{18} = \frac{2}{11} }$

Which is of the form p/q where p , q are integers and q ≠ 0

Given :

The number $\displaystyle \sf{ 0. \overline{18} }$

To find :

To express in the form p/q where p , q are integers and q ≠ 0

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. \overline{18} }$

Step 2 of 2 :

Express in the form p/q where p , q are integers and q ≠ 0

$\displaystyle \sf{ Let \: \: x = 0. \overline{18} }$

Then x = 0.18181818... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 18.18181818... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 18

$\displaystyle \sf{ \implies x = \frac{18}{99} }$

$\displaystyle \sf{ \implies x = \frac{2 }{11} }$

$\displaystyle \sf{ \therefore \: \: 0. \overline{18} = \frac{2}{11}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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