9 Marks Q-9 Express 0.99999... in the formp/q and discuss why the answer makes sense.
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Answer:
Lets’s assume
x = 0.99999……
10x = 9.99999….
Hence,
10x – x = (9.99999…..) – (0.99999……..)
9x = 9
x = 1
As, 0.9999….. just goes on,
At some point of time there is no gap between 1 and 0.9999….
We note that, 0.999 is too much near 1, hence, 1 is justified as the answer.
Hence, x is in the form p/q, where p and q are integers and q ≠ 0.
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