2.91 π
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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 <math.h>, 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?
float number:
B. What is the fractional binary representation of 22/7?
22/7=3+1/7
C. At what bit position (relative to the binary point) do these two approximations to π diverge?
9th
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