How do you get an irrational number between 0.6 and 0.66? - Answers

A rational, non-zero number multiplied by an irrational number always results in an irrational number. Knowing this, you can fairly easily choose a rational number to multiply by any given irrational that will be within your stated range. In this example, I'm going to choose pi (~3.1415926535897932) as the irrational number and x will be the rational number. So we want to satisfying the following inequality: 0.6 < pi * x < 0.66 Dividing everything by pi (which is positive) gives us: 0.6/pi < x < 0.66/pi A quick check on the calculator tells us that: 0.6/pi ~= 0.191 0.66/pi ~= 0.21 So, choosing x = 0.20, we end up with 0.2 * pi as our answer. A quick verification with the calculator shows that 0.2 * pi ~= 0.628, so it's between 0.6 and 0.66. Since 0.2 is 1/5, the equivalent pi/5 is a slightly more aesthetic answer.