Question

Repeating decimal 10.363636...simplest fractional form p/q, find the value of p+q

Answer 1

let x= 10.363636....-----(1)
multiply (1) with 100
100x =1036.363636....---(2)
subtract (1) from (2)
99x= 1026
x=1026/99
after cancellation
x=114/11=p/q

p+q=114+11=125

Answer 2

Answer:

$\frac{p}{q}=\frac{114}{11}$

p+q=125      

Step-by-step explanation:

Given : Repeating decimal 10.363636...

To find : Simplest fractional form p/q, find the value of p+q?

Solution :

Let $y=10.363636...$ ....(1)

Multiply both side by 100,

$100y=1036.3636......$ .....(2)

Subtract (1) and (2),

$100y-y=(1036.3636......)-(10.363636...)$

$99y=1026$

$y=\frac{1026}{99}$

$y=\frac{114}{11}$

So, The p/q form is $\frac{p}{q}=\frac{114}{11}$

Here, p=114 and q=11.

So, p+q=114+11=125.