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Question
Express 0.99999 .... in the form `p/q`. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.
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Solution
Let x = 0.99999...... ...(1)
Multiplying both sides by 10 (since one digit is repeating), we get
10x = 9.9999...... ...(2)
(2) - (1)
⇒ 10x - x = 9
⇒ 9x = 9
⇒ x = `9/9` = 1
Thus 0.99999....... = 1
= `1/1`
Here p = 1, q = 1
As 0.99999..... goes on forever, there is no such a big difference between 1 and 0.99999.......
Hence, they are equal.
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