Question

Express 0.99999.... in the form p/q .Are you surprised by your answer? With your teacher and classmates discuss why the answers makes sense
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Answer 1

Given:

0.9 = 0.99999…

Let x = 0.99999……. (1)

Here only one digit is repeating so multiply by 10 on both sides

10 × x = 10× 0.99999….

10x = 9.9999…. (2)

On subtracting equation 1 from equation 2

10x- x = 9.9999…. - 0.9999….

9x = 9

x = 9/ 9 = 1

Here , 0.9 = 1

Yes we are surprised to get an integer 1, because 0.9999…. goes on forever so there is no gap between 1 and 0.999 9... and hence they are equal.

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Hope this will help you ...

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.