Question

please answer that question ​

Answer 1

Topic

Number System

To Convert

0.47777..... into p/q fraction.

Understanding the Question

We can't directly write it into p/q form. So, we will have to use some manipulation to get the answer.

Solution

Let p/q form be x.

So, x = 0.47777.....

Now, multiply x with 10.

On multiplying we get,

10x = 10 × 0.47777....

10x = 4.777777.....

Now, multiply x with 100.

On multiplying we get,

100x = 100 × 0.4777...

100x = 47.7777.......

Now, subtract 10x from 100x :-

100x - 10x = 90x

( 47.7777.... ) - ( 4.7777.... ) = 90x

43 = 90x

x = 43/90

Answer

So, p/q form of 0.47777.... is 43/90.

Verification

Divide 43 by 90.

It comes out to be 0.4777777....

Hence, Verified.