SOLUTION: how to show some number is a rational number?? example.. a) 2.01414141414......

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Question 459062: how to show some number is a rational number??
example..
a) 2.01414141414......
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+2.014141414..... =
2+%2B+.1%2A.14141414.....
Looking only at the .14141414.....
I'll say:
(1) y+=+.14141414.....
(2) +100y+=+14.14141414.....
Subtract (1) from (2)
(2) +100y+=+14.14141414.....
(1) y+=+.14141414.....
+100y+-+y+=+14+
+99y+=+14+
+y+=+14%2F99+
Now I can say:
2.014141414..... = +2+%2B+.1%2A%2814%2F99%29+
2.014141414..... = +2+%2B+14%2F990+
2.014141414..... = +1994%2F990+
It is rational