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.

Answer 1

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

Since 0.99999............goes on for ever, so there is no gap between 1 and 0.99999........ and hence they are equal