### Instruction: How many positive integers are less than $100\pi$?### Response: 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 $100\pi$.