Question

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

Answer 1

$\frac{25}{48}$ 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

$\frac{11}{40} = 0.275$

So here the decimal part is not repeating. So $\frac{11}{40}$ does not represent repeating decimal

Option 2

$\frac{3}{25} =0.12$

So here the decimal part is not repeating. So $\frac{3}{25}$ does not represent repeating decimal

Option 3

$\frac{25}{48} = 0.52083333333$

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

So $\frac{25}{48}$ represents repeating decimal

Option 4

$\frac{7}{32} = 0.21875$

So here the decimal part is not repeating. So $\frac{7}{32}$ does not represent repeating decimal