Question

Show that 0.5353535353...can be expressed in the form p/q, where p and q
are integers and q * 0​

Answer 1

Answer:

53/99

Step-by-step explanation:

x = 0.5353

now here, two digits (5 and 3) are being repeated continuously hence we will take two zeroes which gives us 100. Then we will multiply 0.5353 with 100

so,

x = 0.5353 (equation 1)

100 x = 53.5353 ( equation 2)

subtract equation 1 from equation 2

100x - x = 99x

53.5353 - 0.5353 = 53

99 x = 53

x = 53/99

53/99 cannot be simplified further, hence it is our final answer.

Therefore, 0.5353... expressed in the form p/q is 53/99

Hope it helps you ❤️