Question

show that 0.2353535..... can be expressed in tha form p/q where p and q are integers and q not = 0.

Answer 1

$x = 0.2353535... \\ 10x = 2.353535... \\ 100x = 23.53535... \\ 1000x = 235.353535... \\ 10x - 1000x = 2.353535... - 235.353535... \\ - 990x = - 233 \\ x = \frac{233}{990} \: \: \: in \: \frac{p}{q} \: form$

Answer 2

Answer:

233/990

Step-by-step explanation:

Here, the given expression is,

0.235353535......

Let y = 0.235353535......  ------(1)

By multiplying 10 on both sides,

We get,

10 y = 2.35353535......., ------(2)

Again, 1000 × equation (1),

We get,

1000 y = 235.353535........ -----(3),

Equation (3) - Equation (2),

990 y = 233

⇒ y = 233/990

Again by equation (1),

$0.235353535...... = \frac{233}{990}$

Where, 233 and 990 are integers such that 990 ≠ 0.