Question

express 0.001...... (non terminating) in the form p/q , where p and q are integers and q not equal to 0

Answer 1

Answer:

0.001...... = 1/999

Step-by-step explanation:

Period = 001

Periodicity = 3

(x = 0.001...) - eq①

(x = 0.001....)*1000

1000x = 1.001001 - eq ②

     Subtract eq① from eq②

1000x = 1.001001....

       x = 0.001001....

1000-x = 1.001001 - 0.001001

 999x = 1

        x = 1/999

Answer 2

Answer:

1/999

Step-by-step explanation:

if x = 0.001....

1000x = 1.001

1000x = 1 + 0.001

1000x = 1 + x

1000x - x = 1

999x = 1

x = 1/999