According to several sources such as Wikipedia and Wolfram Alpha, this is an open question. In fact, there is no pair of non-zero integers m and n for which it is known whether mπ + ne is irrational or not.
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Yes. Example: pi - pi = 0.You can even subtract two different irrational numbers to get a rational number.For example: e - (e - 1) = 1 or Φ - (1/Φ) = 1.
If it would never end, then it is irrational e.g. 10/3 = 3.33333333... etc.. if it ends it's rational e.g. 1000/8 = 125 other irrational numbers: pi, e
5, -7.986543, 37/91, sqrt(64), 193 are all rational. sqrt(2), pi, e, cuberoot(32) are all irrational.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
No it is rational because 0.3 is equal to 3/10, both integers. Examples of irrational numbers are pi, e, or sqrt(2).