Question

Express 0.99999 ....in the form p/q . are you suprised by your answer? with your teacher and classmate discuss why the answer makes sense

Answer 1

No,Im not Surprised.

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

Assume that x = 0.9999…..Eq (a)

Multiplying both sides by 10,

10x = 9.9999…. Eq. (b)

Eq.(b) - Eq.(a), we get

10x = 9.9999…

x = 0.9999…

9x = 9

x = 1

The difference between 1 and 0.999999 is 0.000001 which is negligible.

Hence, we can conclude that, 0.999 is too much near 1, therefore, 1 as the answer can be justified.