Question

Which of the following rational numbers represents a repeating decimal 11 / 40 ,3/25, 25/48,or 7/32

Answer 1

`(25)/(48)` represents repeating decimal

Solution:

We are asked to find the rational number that represents repeating decimal

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely)

Option 1

`(11)/(40) = 0.275`

So here the decimal part is not repeating. So
`(11)/(40)` does not represent repeating decimal

Option 2

`(3)/(25) =0.12`

So here the decimal part is not repeating. So
`(3)/(25)` does not represent repeating decimal

Option 3

`(25)/(48) = 0.52083333333`

So here in decimal part "3" is repeating and goes on forever

So
`(25)/(48)` represents repeating decimal

Option 4

`(7)/(32) = 0.21875`

So here the decimal part is not repeating. So
`(7)/(32)` does not represent repeating decimal