If $x$ is a number between 0 and 1, which of the following represents the smallest value?

A). $x$
B). $x^2$
C). $2x$
D). $\sqrt{x}$
E). $\frac{1}{x}$

Express your answer as A, B, C, D, or E.
Since $0 < x < 1,$
\[x^2 < x < 2x,\]and $x^2 < x < \sqrt{x}$ and $x < 1 < \frac{1}{x}.$  Therefore, the smallest number is always $x^2,$ and the answer is $\boxed{\text{B}}.$