Question

Question 4
Express 0.99999…in the form $\frac{p}{q}$. Are you surprised by your answer? Discuss why the answer makes sense.

Answer 1

Let x = 0.9999…
10x = 9.9999… (Since there is only one repeating digit after the decimal, thus multiply x by 10)
10x = 9 + x
9x = 9
x = 1
The difference between 1 and 0.999999 is 0.000001 which is negligible.
Thus, 0.999... is too near to 1.
Therefore, 1 can be justified as the answer.