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Is e to the pi rational?


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Answered 2010-11-26 04:21:41

e^pi ~ 23.14069.............., not rational

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It is NOT rational, but it IS real.Start with Euler's formula: e^ix = cos(x) + i*sin(x) for all x.When x = pi/2,e^(i*pi/2) = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = ior i = e^(i*pi/2)Raising both sides to the power i givesi^i = e^[i*(i*pi/2)] = e^[i*i*pi/2]and since i*i = -1,i^i = e^(-pi/2) = 0.20788, approx.


Because numbers such as pi, e and the square root of 2 are not rational.


A rational number is able to be represented as a ratio of polynomials. pi/e is a ratio of irrational numbers, neither of which can be represented as a ratio of polynomials, and so I would conclude that pi/e is not rational. But it's a good question, because what if two irrational numbers could cancel out their irrationality, like two negative numbers! A quotient of two irrational numbers can be a rational number. Trivial example 2pi/pi = 2.


3.14 is a rational number pi is not. pi is not 3.14


Pi is not rational it is irrational because it does not stop or repeat


(pi) itself is an irrational number. The only multiples of it that can be rational are (pi) x (a rational number/pi) .


Yes. All rational numbers must terminate or repeat. Rational: 1/3, 1/8, 13, 0.6666666666666... Not rational: π (pi), e, √2


No, it is not.


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.


Assuming that you mean pi, and not pie, it is not a rational number.The set of rational numbers is a field and this means that for every non-zero rational number, there exists a multiplicative inverse in the setand also, due to closure, the product of any two rational numbers is a rational number.Now suppose 7*pi were rational.7 is rational and so there is its multiplicative inverse, which is (1/7).(1/7) is also rational so (1/7)*(7*pi) is rationalBut by the associative property, this is (1/7*7)*pi = 1*pi = pi.But it has been proven that pi is irrational. Therefore the supposition must be wrong ie 7*pi is not rational.


No 10*pi is not a rational number because it can't be expressed as a fraction


Yes. For example, if you take any truncated equivalent of pi then it will be rational.


It the radius is r then the area is pi*r*r - which is pi times a rational number. pi is an irrational number, so the multiple of pi and a rational number is irrational.


Consider pi and 4 - pi. 4 - pi + pi = 4, which is clearly rational. However, both pi and 4 - pi are irrational, as you can verify. plz to be lerning numburs Then consider pi + pi = 2pi, which is clearly irrational. The sum of two irrational numbers, therefore, may or may not be rational.


Any multiple of or addition to or subtraction from PI is an irrational number. PI divided by PI is 1, a rational number. So is PI times 0 = 0


No 22*pi is not a rational number


Minus pi. Or minus pi plus any rational number. Here is how you can figure this out (call your unknown number "x", and let "r" stand for any rational number):x + pi = r To solve for "x", simply subtract pi from both sides. That gives you: x = r - pi


O.325 is a rational number due to the fact you can write it... Pi or e on the other hand never end and therefore are irrational numbers.


Yes. 2*pi is irrational, pi is irrational, but their quotient is 2pi/pi = 2: not only rational, but integer.


Here is an example sentence with the word "rational":Any number that is recurring is classified as a rationalnumber.And as a bit of a laugh:3.14 to Pi: Be rational!Pi to 3.14: Be real!



A rational number is a fraction with an integer in the numerator, and a non-zero integer in the denominator. If you consider pi/2, pi/3, pi/4 (common 'fractions' of pi used in trigonometry) to be 'fractions', then these are not rational numbers.


No; since pi is irrational if you multiply it by a rational number it is still irrational


No. For example, pi/2 is a fraction which is not rational.


no every periodic number is rational but pi is irrational



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