$0 < a < 1$. Which of the following are true?

I. $a^{2} < a$

II. $\sqrt{a} > a$

III. $\frac{1}{a} < 1$

IV. $a^{3} < a^{2}$

Explanation

1. 01

   Multiplying by $a$, a number between 0 and 1, makes things smaller: $a^{2} < a$ and $a^{3} < a^{2}$. And $\sqrt{a} > a$, as with $\sqrt{0.25} = 0.5$.

2. 02

   III is false: $\frac{1}{a} > 1$, as with $\frac{1}{0.5} = 2$.