Question

show that 0.2353535=0.235 3&5 on bar can be expressed in the form p/q where p and q are integers and q ≠0

Answer 1

Solution of your problem is that 0.235 bar on 35 can be written as 233/990.

Answer 2

$\underline{\bold{Answer :}}$

Answer is 233 / 990

Solution :

$\sf 0.2 \overline{35}$

Let x = $\sf 0.2 \overline{35}$

⇒ x = 0. 23 53 53 535........( i )

Multiply both sides by 10,

⇒ 10x = 2. 35 35 35 35...... ( ii )

Multiply both sides by 100,

⇒ 1000 x = 235. 35 35 35...... ( iii )

On subtracting ( ii ) from ( iii )

1000 x - 10 x = 235 - 2

⇒ 990 x = 233

⇒ x = $\sf \frac{233} {990}$

Therefore, $\sf 0.2 \overline{35} = \frac{233} {990}$