Question

Express 0.999999 in the form of p/q

Answer 1

Answer:

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.

Hope this will help you ...

Step-by-step explanation:

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