Question

Express 2.313131 into P by Q form​

Answer 1

Answer:

Step-by-step explanation:

2.313131 = 2.31_

Let x = 2.3131......... Equation 1

Since two two digits are repeating so we multiply equation 1 by 100

=100x = 231.3131...... Equation 2

on subtracting equation 1 from equation 2 we get

100x - x = 231.3131... - 2.31...

99x = 229

x =229/99

X= 229 / 99 ANSWER

Answer 2

Answer:

The  $\frac{p}{q}$ form of 2.313131......................= $\frac{229}{99}$  

Step-by-step explanation:

Given decimal number is 2.313131.............

To find,

The $\frac{p}{q}$ form of the given rational number

Solution:

Let x = 2.313131..................(1)

'x' is a recurring decimal. Hence there are two recurring decimal places,

Multiply the equation(1) by 100 on both sides

100x = 100 ×2.313131......................

100x = 231.3131...................(2)

To eliminate the recurring decimal places, subtract equation(1) from equation (2) we get

100x - x = 231.3131..................... - 2.3131................

99x = 229

x = $\frac{229}{99}$

Then we have, 2.313131......................= $\frac{229}{99}$

The  $\frac{p}{q}$ form of 2.313131......................= $\frac{229}{99}$  

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