Question

Which of the following is a rational number between $\frac{1}{4}$ and $\frac{1}{3}$?

• A. 0
• B. $\frac{1}{8}$
• C. $\frac{7}{25}$
• D. $\frac{1}{5}$

Answer 1

The correct option is C

$\frac{7}{25}$

The decimal expansion of $\frac{1}{4}$ is 0.25 and the decimal expansion of $\frac{1}{3}$ is 0.333...

Now comparing with the decimal expansion 0.25 and 0.333... with the options:
a) Clearly, 0 is out of the range.
b) The decimal expansion of $\frac{1}{8}$ is 0.125 which is also out of the range.
c) The decimal expansion of $\frac{7}{25}$ is 0.28, so it lies between $\frac{1}{4}$ and $\frac{1}{3}$ .
d) The decimal expansion of $\frac{1}{5}$ is 0.2, so it is out of the range.