Question

If 2.161616............is written as p/q, such that p and q are positive integers without any
common factor, find the value of p + q.​

Answer 1

Answer:

Let x = 2.1616....(1)

Since there are 2 recurring digits, multiply both sides with 10^2 (10^2 = 100)

100x = 2.1616×100

=> 100x= 216.16.....(2)

Subtract (1) from (2)

=> (2) - (1) = 99x = 214.0

=> x = 214/99

p = 214, q = 99

Hence, p+q = 214+99 = 313

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