Question

When the repeating decimal 10.363636 .... is written in simplest fractional form p/q, find

the value of p + q.​

Answer 1

Answer:

10.363636

Let us take that the above number is equal to some variable as below:

x=10.363636……(1)

Now multiply both sides by 100 as below:

100×x=10.363636×10

100x=1036.363636….(2)

Next subtract equation (2) from equation (1) as below:

100x−x=1036.3636363−10.363636⇒99x=1026⇒x=102699

Now we can simplify the above fraction by dividing numerator and denominator by 3 as follows:

x=10263993∴x=11411

So 10.363636 is written as 11411 in the simplest fraction form.

Comparing 11411 by pq we get,

p=114q=11….(3)

Finally we have to find the value of:

p+q

Equate the value from equation (3) above we get,

p+q=114+11∴p+q=125

Hence value of p+q is 125.