Question

Show that 0.2353535... = 0.235 can be expressed in the form p/q, where p and q are integers and q ≠ 0.​

Answer 1

Answer:

Answer: 0.2353535... = 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero.

Answer 2

A rational number can have two types of decimal representations (expansions):

• Terminating

• Non-terminating but repeating

0.2353535... is a non-terminating but repeating decimal, it is denoted by 0.2¯350.235¯.

let x = 0.2353535...

100x = 235.353535...

100x - x = (235.353535...) - (2.353535...)

99x = 233

x = 233/99

Therefore, 0.2353535... = 0.235... = 233/99 can be expressed in the rational form.

Thus, 0.2353535...= 0.235 can be expressed as 233/99 i.e., in the form of p/q, where p and q are integers and q is not equal to zero