Question

Express 2.36bar➕0.23bar in p/q form where p and q are integers

Answer 1

2.36bar and 0.23bar are non terminating or non recurring numbers . non terminating numbers are irrational so they can't be written in the form of p/q form.

Answer 2

Answer:

Number in p/q form is $2.\bar{36}+0.\bar{23}=\frac{257}{99}$

Step-by-step explanation:

Given : Number 2.36bar+0.23bar

To find : Express number bar in p/q form ?

Solution :

Let $x=2.\bar{36}$

$x=2.363636...$ .....(1)

Multiply equation (1) by 100,

$100x=236.3636...$ ......(2)

Subtract equation (1) and (2),

$100x-x=(236.3636...)-(2.363636...)$

$99x=234$

$x=\frac{234}{99}$

Let $y=0.\bar{23}$

$y=0.232323...$ .....(3)

Multiply equation (3) by 100,

$100y=23.232323...$ ......(4)

Subtract equation (3) and (4),

$100y-y=(23.232323...)-(0.232323....)$

$99y=23$

$y=\frac{23}{99}$

So, $2.\bar{36}+0.\bar{23}=\frac{234}{99}+\frac{23}{99}$

$2.\bar{36}+0.\bar{23}=\frac{234+23}{99}$

$2.\bar{36}+0.\bar{23}=\frac{257}{99}$

Therefore, Number in p/q form is $2.\bar{36}+0.\bar{23}=\frac{257}{99}$