Question

The rational number between $\frac{1}{4}$ and $\frac{1}{3}$ is .

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

Answer 1

The correct option is A $\frac{7}{25}$

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) The decimal expansion of $\frac{1}{8}$ is 0.125 which does not lie between 0.25 and 0.333.... .

b) The decimal expansion of $\frac{7}{25}$ is 0.28, so it lies between $\frac{1}{4}$ and $\frac{1}{3}$ .

c) The decimal expansion of $\frac{1}{5}$ is 0.2, which does not lie between 0.25 and 0.333.... .