Question

Express 23.43434343.....in p/q form where p,q are integers and q is not equal to 0

Answer 1

Let X = 23.434343...........
 100 X = 2343.434343....... (because after the point there r 2 numbres repeating so multiply with 100)
    100 X - X = 2343.434343....... - 23.43434......
    99 X = 2320
     X = 2320/99 
  so p= 2320 
      q = 99

Answer 2

$\displaystyle \sf{23.43434343... = \frac{2320}{99} }$

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

Given :

The number 23.43434343...

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 23.43434343...

Step 2 of 2 :

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

Let x = 23.43434343... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 2343.43434343... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 2320

$\displaystyle \sf{ \implies x = \frac{2320}{99} }$

$\displaystyle \sf{ \therefore \: \: 23.43434343... = \frac{2320}{99} }$

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