Question

express 1.32 bar in p/q form....?

Answer 1

x = 1.3222.......

10 x = 13.2222 .... -> (1)

100 x = 132.2222..... ->(2)

Subtracting 1) from 2)

100 x - 10x = 132.222 - 13.222

90 x = 119

x = 119/90

Answer 2

$\displaystyle \bf{ 1. \overline{32} = \frac{131}{99} }$

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

Given :

The number $\displaystyle \sf{ 1. \overline{32} }$

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 $\displaystyle \sf{ 1. \overline{32} }$

Step 2 of 2 :

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

$\displaystyle \sf{ Let \: \: x = 1. \overline{32} }$

Then x = 1.323232... - - - - - - - (1)

Multiplying both sides by 100 we get

100x = 132.323232... - - - - - - (2)

Equation 2 - Equation 1 gives

99x = 131

$\displaystyle \sf{ \implies x = \frac{131}{99} }$

$\displaystyle \sf{ \therefore \: \: 1. \overline{32} = \frac{131}{99}}$

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

Correct question : Express $\displaystyle \sf{ 1. \overline{32} }$ in p/q form

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