Question

convert 0.2222...... in p/q form with steps​

Answer 1

Answer:

Step-by-step explanation:

X = 0.2222...

10x = 2.222...

10x = 2.222...

-x = -0.222...

.............................

9x = 2

X= 2\9

Answer 2

Step-by-step explanation:

Why to convert in p/q form?

So, the given number is a rational number, and we know that rational numbers can be expressed in the p/q form.

So, the given number is 0.22222222.......

As, 2 is terminating, therefore 0.22222.... is a rational number.

Coming to our question, we've to convert it into p/q form.

Now,

$\rm let\ x=0.2222222..... --(1)\\ \\ \rm Multiplying\ both\ sides\ by\ 10,\ we\ get\\ \\ \rm 10x=2.222222222...... --(2)\\ \\ \rm Subtracting,\ eq.\ (1)\ by\ (2)\\ \\ \rm 10x-x=(2.2222222......)-(0.222222.....)\\ \\ \rm \implies 9x=2\\ \\ \rm \therefore x=\frac{2}{9}\\ \\ \therefore (0.22222......)=\frac{2}{9} \\ \\ \text{It means that, if you divide 2 by 9, you'll get (0.22222....)}$