Question

convert the form of p/q 2.181818...........​

Answer 1

Answer: 24/11

Step-by-step explanation:

Let x = 2.181818...     (1)

Multiply both sides by 100

100*x = 2.181818...*100

100x = 218.181818...    (2)

Subtract (1) from (2)

100x - x = 218.181818... - 2.181818

99x = 216

x = $\frac{216}{99}$

x = $\frac{24}{11}$

∴ 2.181818..... = 24/11

Answer 2

Answer:-

Let x = 2.181818..... - equation 1

Here periodicity is 2.

So multiply 100 on both the sides.

100 × x = 100 × 2.181818.....

100x = 218.181818.... - equation 2

Subtract equation 1 from equation 2.

100x = 218.181818.... - x= 2.181818.......

=> 99x = 216

$x = \frac{216}{99}$

Answer :-

$\frac{216}{99}$