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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.
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