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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Answered by
9
Answer:
let x = 2.161616....
then 100x = 216.1616......
now 100x - x = 216.1616..... - 2.161616....
99x = 214
x = 214/99
that means p= 214 and q = 99
p+q = 313
Answered by
7
Let, x = 2.161616......
Then 100x = 216.161616......
Now, 100x - x = 216.161616...... - 2.161616......
or, 99x = 214
or, x = 214/99
Therefore, 2.161616...... = 214/99
This is the required fraction. Comparing it with p/q, we can write
- p = 214
- q = 99
They have no common factors.
Therefore, p + q = 214 + 99
= 313.
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