Question

Q.10 Show that 0.45 = 0.454545…. can be expressed in the form pq where p and q are integers       and q ≠ 0. ​

Answer 1

Answer:

5/11

Step-by-step explanation:

Let x  be 0.454545454545

x= 0.454545454545[1]

10x= 4.54545454545

100x= 45.4545454545[2]

subtract eq 1 from 2

100x−x= 45.4545454545[2] −0.454545454545[1]

99x= 45

11x=5

x=5/11

Answer 2

Step-by-step explanation:
Let 0.454545...= x
Since there are two numbers repeating,
100x = 0.454545 x 100
100x= 45.4545
100x= 45.454545...= 45+0.454545....
100x = 45.454545...= 45+x
100x=45+ x
Bringing x from RHS to LHS
100x - x = 45
99x = 45
Bringing 99 from LHS to RHS
x = 45/99
45/99 is your answer!
Hope it helps!