How many positive integers are less than $100\pi$?
To answer this question, I need to find the largest positive integer that is less than $100\pi$. I can use a calculator to get an approximation of $100\pi$, which is about 314.16. So, the largest positive integer that is less than $100\pi$ is 314. Therefore, there are 314 positive integers that are less than $100\pi$. 