Question

show that 0.235 bar can be expressed in the form of p by q where p and q are integers and q is not equal to zero and

Answer 1

x=0.235 bar ----(1)
as there is bar on two digits
100*x= 100*0.235
100x =23.5 ---(2)
subtracting (1) from (2)
100x - x =23.5 - 0.235
99x = 23.335
x = 23.335/99
x = 23335/99000

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