# 2.91 π **Problem**: Around 250 B.C., the Greek mathematician Arichimedes proved that 223/71 < π < 22/7. Had he had access to a computer and the standard library ``, he would have been able to determine that the single-precision floating-point approximation of π has the hexadecimal representation `0x40490FDB`. Of course, all of these are just approximations, since π is not rational. A. What is the fractional binary number denoted by this floating-point value? ``` 0 10000000 10010010000111111011011 ``` float number: ``` 0b11.0010010000111111011011 ``` B. What is the fractional binary representation of 22/7? 22/7=3+1/7 ``` 0b11.001001001(001)... ``` C. At what bit position (relative to the binary point) do these two approximations to π diverge? 9th --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://valineliu.gitbook.io/deuterium-wiki/reading/cs-jing-dian-shu-ji/csapp-3e-homework-solution/2.-representing-and-manipulating-information/2.91-p.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.