Question

2. Write p/q form of 1.9999........​

Answer 1

Answer:

The answer is given below

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Explanation:

x = 1.9999.....

10x = 19.9999.......

10x = 18 + 1.9999.....

10x = 18 + x

10x - x = 18

9 = 18

x = 18/9 = 2

1.9999 = p/q = 2

Answer 2

Answer:

2/1

Explanation:

Let x be the p/q form of 1.9999......

thus, x = 1.9999.... (eqn i )

10x = 1.9999.....×10 = 19.9999.. (eqn ii )

Subtracting eqn (i) from eqn (ii)

=> 10x = 19.9999....

- x = 1.9999....

9x = 18

thus, x = 18/9 = 2/1