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.
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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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