Question

Which is a closer estimate of pi? Explain your answer.

Answer 1

The fraction 22/7 has a value of 3.142857, so it has the same first three digits as pi. Both 3.14 and 22/7 are approximations of pi. In fact, 22/7 is close to pi than 3.14 is. Pi is irrational. That is, the decimal expansion never ends and never repeats, so any number of decimal places we wrote out is an approximation. The approximation 3.14 is about 1/2 percent off from the true value, and the fairly well know 3.141559 is within 0.000084 percent.