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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.
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Is e to the pi rational?
e^pi ~ 23.14069.............., not rational
Is pi divided by 2 rational or irrational?
If a numerator and/or denominator in a fraction is irrational, the entire fraction is irrational. Since pi is irrational, pi divided by two is also irrational.
If pi is irrational does that mean that pi divided by 2 is irrational?
Yes, it does. If Pi/2 were rational, it could be written as p/q, and then Pi could be written as 2p/q and would be rational as well.
What are Two nine digit numbers divided to equal pi?
No two numbers that can be completely written down with digits can be added, subtracted, multiplied, or divided to equal PI. If they could be divided to equal PI, then PI would be a rational number. But it isn't.
Why is pi rational?
Pi is not rational it is irrational because it does not stop or repeat
Is e to the pi rational?
e^pi ~ 23.14069.............., not rational
Is pi 12 equal to a rational number?
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
Is pi divided by 2 rational or irrational?
If a numerator and/or denominator in a fraction is irrational, the entire fraction is irrational. Since pi is irrational, pi divided by two is also irrational.
Is an irrational number divided by an irrational number always a rational?
No. sqrt(2)/pi is not rational.
If pi is irrational does that mean that pi divided by 2 is irrational?
Yes, it does. If Pi/2 were rational, it could be written as p/q, and then Pi could be written as 2p/q and would be rational as well.
How can you make rational of i power i?
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.
What are Two nine digit numbers divided to equal pi?
No two numbers that can be completely written down with digits can be added, subtracted, multiplied, or divided to equal PI. If they could be divided to equal PI, then PI would be a rational number. But it isn't.
Why rational numbers require extension?
Because numbers such as pi, e and the square root of 2 are not rational.
Is 0.0125 rational?
Yes. All rational numbers must terminate or repeat. Rational: 1/3, 1/8, 13, 0.6666666666666... Not rational: π (pi), e, √2
Is 3.14 a rational or irrational number?
3.14 is a rational number pi is not. pi is not 3.14
Why is pi rational?
Pi is not rational it is irrational because it does not stop or repeat
Can you subtract 2 irrational numbers to get a rational number?
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.
