Question

Express 0.818181… in the form of p/q

Answer 1

Step-by-step explanation:

Let a = 0.818181... = 0.81 bar

So, 100a = 81.81 bar

Thus,

100a - a =81.81 bar - 0.81 bar

99a = 81

a = 81/99

Answer 2

$\displaystyle \sf{0.818181… = \frac{9}{11} }$

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

Given :

The number 0.818181…

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 0.818181…

Step 2 of 2 :

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

Let x = 0.818181… - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 81.818181… - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 81

$\displaystyle \sf{ \implies x = \frac{81}{99} }$

$\displaystyle \sf{ \implies x = \frac{9}{11} }$

$\displaystyle \sf{ \therefore \: \: 0.818181…. = \frac{9}{11} }$

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