Question

the rational number of the form p/q, where q is not equal to 0, p and q are positive integers which represents 0.1343434343434......... is

Answer 1

let x=0.134343434.......... (1)
multiplying by 10 we ge
10x=1.34343434................ (2)
multiplying by 100 we get
100x=134.343434..... (3)
Subtracting (2) from (3) we get
90x=133
x=133/90

Answer 2

Given:

0.1343434343434...

To Find:

In the form of p/q

Solution:

To express in the form of p/q we will let the given number be equal to x. Please note that it can be expressed in p/q form only if the decimal is repeating non terminating decimals. now let x=0.1343434...

$x=0.1343434...$

Now multiply both sides by 10

$10x=1.343434...$      -(1)

Now multiply both sides by 100( we choose it to multiply by 10 100 1000 etc depending on the digits after which they are repeating if they are repeating after 4 digits then multiply by 10000)

$1000x=134.343434...$      -(2)

Now subtracting equation 2 with 1 we have

$990x=133\\x=\frac{133}{990}$

Hence, the number 0.134343... in the form of p/q is 133/990.