Question

express 0.33333............. in p/q form

Answer 1

X=0.33...

10x= 3.33...

10x-x=3.333...-0.333....

9x=3

X=1/3

Answer 2

$\displaystyle \sf{0.33333... = \frac{1}{3} }$

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

Given :

The number 0.33333...

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 0.33333...

Step 2 of 2 :

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

Let x = 0.33333... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 3.33333... - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 3

$\displaystyle \sf{ \implies x = \frac{3}{9} }$

$\displaystyle \sf{ \implies x = \frac{1 }{3} }$

$\displaystyle \sf{ \therefore \: \: 0.33333... = \frac{1}{3} }$

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