Question

Express 0.2 in the form of p/q,where p and q are integers and q is not equal to zero Ans. Let =x=0.2
Mult by 10 10x=2.22...
Subi)from ii)
10x-x=2.22...-0.2...
9x=2
x=2/9

Answer 1

$\displaystyle \bf{ 0. \overline{2} = \frac{2}{9} }$

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

Given :

The number $\displaystyle \sf{ 0. \overline{2} }$

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 $\displaystyle \sf{ 0.\overline{2} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 0. \overline{2} }$

Then x = 0.222222... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 2.222222... - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 2

$\displaystyle \sf{ \implies x = \frac{2}{9} }$

$\displaystyle \sf{ \implies x = \frac{2 }{9} }$

$\displaystyle \sf{ \therefore \: \: 0. \overline{2} = \frac{2}{9}}$

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

Correct question : Express $\displaystyle \sf{ 0.\overline{2} }$ in the form of p/q,where p and q are integers and q is not equal to zero

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