Question

Find the value of 1.999..... in the form p/q , where p and q are integers and q ≠ 0​

Answer 1

Let X = 1.9999....... ---------- (1)

Here, The bar is only for 9, that implies, we have to multiply both sides by 10.

10 × X = 1.999... × 10

10X = 19.9999.....--------(2)

Subtracting (1) from (2), we get,

10X - X = 19.999... - 1.999...

9X = 18

X = 18/9

Therefore, X = 2 (or) 18/9.

Hope it helps you!