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

Convert 0.99999 in p/q form

let $x=0.99999...$ …………………..(1)

Here is only one repeating digit 9 after decimal point so we multiply both sides by 10

$10x=9.99999...$ …………………….(2)

Subtracting (1) from (2)

$$\begin{gathered} 10x-x=\left(9.99999...\right)-\left(0.99999....\right) \\ 9x=9 \\ x=1 \end{gathered}$$

Hence the answer is 1 and it make sense because 0.999… goes on forever so there is no gap between 1 and 0.9999… and hence they are equal .