Question

Please tell me the answer

Answer 1

Question: Represent the following in the form of p / q

(1) 33.2222...... infinity

let,

x = 33.2222..... -----eqn (1)

multiplying by 10 both sides

10 x = 332.2222..... ----- eqn (2)

subtracting eqn (1) from eqn (2) we will get

9 x = 299

x = 299 / 9

which is in the form of p/ q.

(2) 152.5353........ infinity

Let,

x = 152.5353...... ----eqn (1)

multiplying by 100 both sides

100x = 15253.5353...... ---- eqn (2)

subtracting eqn (1) from (2)

99 x = 15101

x = 15101 / 99

( represented in the form p/q)

(3) 1.579577957779....infinity

Here we can see that digits are not occuring repeatedly , this means it is non terminating non recurring decimal expansion

hence it is irrational and can't be expressed in the form p/q.

(4) 1.92222...... infinity

Let,

x = 1.92222.....

multiplying by 10 both sides

10 x = 19.2222...... -----eqn(1)

multiplying again by 10 both sides

100 x = 192.2222...... -----eqn (2)

subtracting eqn(1) from eqn (2)

90 x = 173

x = 173 / 90

(expressed in the form p/q)

(5) 1.621621621..... infinity

x = 1.621621621...... ----- eqn(1)

multiplying by 1000 both sides

1000 x = 1621.621621621..... -----eqn(2)

subtracting eqn (1) from eqn(2)

999 x = 1620

x = 1620 / 999

(simplifying)

x = 540/333

x = 180/111

x = 60 / 37

( represented in the form p/q)