Question

when the repeating decimal 10.363636....is written in simplest fractional from p/q, find the value of p+q

Answer 1

Answer :

Let, x = 10.363636...

Then, 100x = 1036.363636...

Now, 100x - x = 1036.363636... - 10.363636...

==> 99x = 1026

==> x = 1026/99

==> x = 114/11, which is in p/q form

Here, p = 114 & q = 11

Therefore, p + q = 114 + 11 = 125

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Answer 2

☺️hey mate! here's your answer!☺️

let "x" be the decimal that is , 10.363636...

so, 100x = 1036.363636...

then, we will substract the smaller number from greater number ,

=> 100x - x = 1036.363636... - 10.363636....

=> 99x = 1026

$= > x = \frac{1026}{99}$

it can be written in more simpler form by dividing both by 3 .

$= > x = \frac{342}{33}$
again , both numerator and denominator are divisible by 3

$= > x = \frac{114}{11}$

so, decimal 10.3636.. in p/q form = 38/11

thus,

p + q = 114 + 11

=> p + q = 125 ...answer

hope it is helpful ✌️!