Question

convert 0.8282.......... into a rational number ​

Answer 1

Question:-

Convert 0.8282.......... into a rational number.

Solution:-

Let the rational number of 0.8282..... be x.

Then,

x= 0.8282... (i)

Since no of digits repeating are 2.

Thus,

100x= 82.8282..... (ii)

Now,

Subtracting both the equation,

$100x - x = 82.8282..... - 0.8282.... \\ = > 99x = 82 \\ = > x = \frac{82}{99}$

Hope you like my answer.