Question

Express the following in the form P/Q where P & Q are integers & Q is not equal to 0.
1. 0.2353535..........​

Answer 1

Answer:

Step-by-step explanation:

Let 0.2353535...be x

x=0.2353535...

100 * x =0.2353535...*100

100x =23.53535...

100x=23.3 + .2353535...(23.3+.23535..=23.53535)

100x=23.3 + x (0.23535..=x)

100x - x =23.3

99x = 23.3

x =23.3/99

x=23.3 * 10/99 * 10

x = 233/990.....shown

Answer 2

SOLUTION:

Let x = 0.2353535... - Eq. 1

Since the Repeating Block has two Digits, 3 & 5, we multiply x by 100 -

Therefore, 100x = 23.5353535..... - Eq. 2

Subtracting x from 100x, we get -

$100x = 23.53535... \\ - x = 0.2353535... \\ = > 99x = 23.300000...... \\ \\ = > 99x = 23.3 \\ therefore \: 99x = \frac{233}{10} \\ = > x = \frac{233}{990}$

CONCLUSION;

0.2353535... = 233/990

HOPE THIS HELPS....