Answer
There is not a smallest positive number. However, there is a smallest positive integer, which is the number 1.
Work Step by Step
There is not a smallest positive number as you can get infinitely close to 0 by increasing the number of decimal places without ever reaching 0. Another way to think about it is that if n is a positive number and $n\gt0$, then $\frac{n}{2}\gt0$, meaning the number can infinitely get smaller.