The normal fraction 100000000000000 / 314159265358979 will express 1/pi to a high accuracy, what normal fraction would express 1/pi exactly, if any?
2007-05-12 02:27:14 · 12 answers · asked by afaleeds 1 in Science & Mathematics ➔ Mathematics
Everyone in this thread has already covered the bases, but let's assume for the sake of argument that 1/pi can be expressed as a normal fraction. (We're going to prove this cannot happen, as a proof by contradiction).
If 1/pi can be expressed as a fraction, then
1/pi = m/n (for integers m and n, and n not equal to 0).
Multiply both sides by n*pi, to get
m = n(pi)
This implies m is some multiple of PI and m is not equal to 0.
If m is some multiple of PI, then m must be an irrational number. This is a contradiction ( m is an integer ).
Therefore, there exists no normal fraction that would express 1/pi exactly.
2007-05-12 03:40:55 · answer #1 · answered by Puggy 7 · 3⤊ 0⤋
No fraction will express 1/pi since the reciprocal would express pi. Since pi is irrational, this is impossible.
2007-05-12 03:54:31 · answer #2 · answered by mathematician 7 · 0⤊ 0⤋
Would just like to mention that Pi belongs to a class of numbers called transcendentals rather than irrational. That is because it is not the solution of a finite polynomial in x with rational coefficients.
Consider x^2=2. solution is irrational. sq rt 2
You cannot construct any such equation for pi no matter how many finite powers of x you use.
e is another transcendental number
2007-05-12 06:08:52 · answer #3 · answered by Anonymous · 0⤊ 0⤋
NO. Pi is an irrational number meaning that you can not express it by an integer nor a fraction.
This holds true for its inverse
2007-05-12 02:33:54 · answer #4 · answered by maussy 7 · 0⤊ 0⤋
No
beacuse pi is irrational one can not represent it as p/q so 1/pi cannot be represented as q/p
22/7 is approximate value of Pi so 7/22 is of 1/pi
2007-05-12 03:00:59 · answer #5 · answered by Mein Hoon Na 7 · 1⤊ 0⤋
As others have said, there is no fraction that will express 1/pi exactly. If there were, then flipping that fration upside down would express pi exactly, and there is no such fraction.
2007-05-12 03:10:57 · answer #6 · answered by Xexyz 2 · 0⤊ 0⤋
No. Pi is an irrational number with an infinite number of non-repeating decimals. Consequently its reciprocal is also irrational.
See also e, â2 etc.
2007-05-12 02:33:18 · answer #7 · answered by Mad Professor 4 · 0⤊ 0⤋
I am sure you have heard about the people who have estimated pi out to several thousand places. I personally don't think there is a solid, exact answer to pi.
2007-05-12 02:33:33 · answer #8 · answered by bikeworks 7 · 0⤊ 0⤋
None. pi is irrational, and so is its reciprocal. It is easy to see that the reciprocal of any irrational number must be irrational.
2007-05-12 02:31:34 · answer #9 · answered by Anonymous · 2⤊ 0⤋
No. That is the point of irrational numbers: they cannot be expressed using a finite number of rational numbers, no matter what is done to them.
2007-05-12 02:31:15 · answer #10 · answered by Vincent G 7 · 6⤊ 0⤋