Question

prove that 0.333.... can be expressed as p/q ​

Answer 1

$\mathsf{Let \:\:x = 0.333...\:\rightarrow\:(1) }$

Multiplying both sides by 10, we get:

$\mathsf{10x = 10 × 0.333...}$

$\mathsf{10x = 3.333...}$

$\mathsf{10x = 3 + 0.333...}$

$\mathsf{ 10x = 3 + x\:[from (1)]}$

$\mathsf{10x - x = 3}$

$\mathsf{9x = 3}$

$\mathsf{x = 3/9}$

$\mathsf{x = 1/3}$

Hence, we can write 0.333.. as 1/3 in the form of p/q