# What is pi as a fraction?

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• What is pi as a fraction?  Answer #1 | 21/04 2015 14:17 Positive: 100 %
Answer #2 | 21/04 2015 21:17 Positive: 100 %
Answer #3 | 20/04 2015 20:02 pi (π) is an irrational number. It can't be represented as the ratio of integers. You can express pi as the ratio of the circumference to the diameter, so: π = circumference / diameter But those can't both be integers. There are several ways to approximate pi. One common one is 22/7, but it is only accurate to 2 decimal places. π ≈ 3.141592653589793238...
Positive: 83.333333333333 %
Answer #4 | 26/04 2015 12:26 I've understood it as a 'transcendental number' of which pi and e are the most famous. There'a a cite that I like which is Clifford Pickover's : The 15 Most Famous Transcendental Numbers.
Positive: 80 %
Answer #5 | 21/04 2015 05:57 As Jeff, Puzzling, Rita, and freond1 have said, it is irrational, and so, not equal to any fraction (i.e., ratio of integers). However, like all irrational numbers, it is the limit of some infinite sequence of rational numbers (fractions). The technique of continued fractions (CF) can be used to produce the "most efficient" such sequence. The usual practice in CFs is to keep all the terms positive, so that any positive integer can appear in it. It is more efficient, for approximation purposes, to allow the terms to have either sign, but restrict them to having absolute value ≥ 2, with the further stipulation that, following any term of ±2, must be a term of the same sign. What are CFs? They are compound fractions that just keep going, usually with all numerators = 1, where you just keep adding a new (reciprocal) fraction to the latest denominator. They are often written as: a+1/b+1/c+1/d+ . . . — meaning: a+1/(b+1/(c+1/(d+ . . . ))) and then the sequence of terms is often written as: [a; b, c, d, . . .] When you truncate the CF at some finite point, you can simplify the resulting finite compound fraction: a/1, (ab+1)/b, (abc+a+c)/(bc+1), . . . For π, the first 10 terms of the sequence are: [3; 7, 16, -294, 3, -4, 5, -15, -3, 2, . . .] the corresponding fractions (obtained by simplifying the compound fractions & taking absolute values) being: 3 / 1 22 / 7 355 / 113 104348 / 33215 312689 / 99532 1146408 / 364913 5419351 / 1725033 80143857 / 25510582 245850922 / 78256779 411557987 / 131002976 . . . Note: The magnitude of the first *omitted* term is a fair measure of the efficiency of the resulting fraction. There is, AFAIK, no easy way to generate these terms for π, but there are other CFs, with non-unit numerators, that do follow a predictable pattern (see Source).
Positive: 75 %
Answer #6 | 26/04 2015 19:26 I've understood it as a 'transcendental number' of which pi and e are the most famous. There'a a cite that I like which is Clifford Pickover's : The 15 Most Famous Transcendental Numbers.
Positive: 75 %
Answer #7 | 23/04 2015 03:37 it isn't, but a close approx. is 22/7
Positive: 75 %
Answer #8 | 23/04 2015 02:28 It is irrational so no fraction
Positive: 66.666666666667 %
Answer #9 | 23/04 2015 01:48 pi has been known to be irrational for a long time. don't be silly.
Positive: 66.666666666667 %
Answer #10 | 26/04 2015 03:11 The idiot who said pi is a rational number doesn't know what he's talking about. Pi IS irrational because it cannot be expressed as the ratio of two integers. This is a very well-known fact about Pi. It has an infinite number of digits at the end. 22/7 is a decent approximation, but it is not exact. There is no answer to your question. Pi is irrational, and therefore cannot be expressed as a fraction.
Positive: 66.666666666667 %
Answer #11 | 24/04 2015 20:48 pi DOES NOT equal 22/7, that is a common mistake.
Positive: 66.666666666667 %
Answer #12 | 20/04 2015 20:01 Pi is irrational and cannot be written as a fraction. It can be approximated using 22/7.
Positive: 66.666666666667 %
Answer #13 | 21/04 2015 03:08 You can only approximate it as a ratio of integers. 355/113 is a good choice, better than 22/7.
Positive: 66.666666666667 %
Answer #14 | 22/04 2015 08:20 pi is a transcendental irrational number but approximations of pi can be expressed as fractions 22/7 (0.0402% off) 355/113 (0.0000008% off)
Positive: 66.666666666667 %
Answer #15 | 20/04 2015 20:08 You can only approximate it as a ratio of integers. 355/113 is a good choice, better than 22/7.
Positive: 66.666666666667 %
Answer #16 | 27/04 2015 04:52 about 22/7, which is more accurate than 3.14 but the most accurate way to get pi is to use the pi symbol.
Positive: 60 %
Answer #17 | 24/04 2015 00:01 there is no exact fraction to represent pi, but a close fraction to pi would be 22/7
Positive: 60 %
Answer #18 | 26/04 2015 23:36 Approximitly 22/7
Positive: 50 %
Answer #19 | 21/04 2015 03:01 Pi is irrational and cannot be written as a fraction. It can be approximated using 22/7.
Positive: 50 %
Answer #20 | 21/04 2015 19:51 Pi is an irrational number, meaning it can't be represented as a fraction.
Positive: 50 %
Answer #21 | 26/04 2015 21:11 we know 1 + x + x^2 + x^3..... = 1/1-x replace x by -x^2 1 - x^2 + x^4 - x^6 = 1/1+x^2 integrate both sides x - x^3/3 +x^5/5 - x^7/7..... = tan^-1(x) put x=1 1 - 1/3 + 1/5 .....= pi/4 so pi = 4/1 - 4/3 + 4/5 - 4/7 ...
Positive: 50 %
Answer #22 | 22/04 2015 02:51 Pi is an irrational number, meaning it can't be represented as a fraction.
Positive: 50 %
Answer #23 | 23/04 2015 07:06 Pi the number is an irrational number that cannot be represented as a fraction of two integers. It is defined as the fraction C/d, where C is the circumference of a circle and d is the diameter, if this was what you were referring to as a fraction.
Positive: 50 %
Answer #24 | 22/04 2015 15:20 pi is a transcendental irrational number but approximations of pi can be expressed as fractions 22/7 (0.0402% off) 355/113 (0.0000008% off)
Positive: 50 %
Answer #25 | 26/04 2015 22:58 Pi is irrational so it cannot be written in fraction. But an approximate value of pi is 22/7
Positive: 50 %
Answer #26 | 21/04 2015 03:02 π = π/1 and π/1 is a fraction. However π does NOT equal a/b for any integers a and b. So, although π is a perfectly good real number, like most real numbers it is irrational.
Positive: 33.333333333333 %
Answer #27 | 27/04 2015 05:58 Pi is irrational so it cannot be written in fraction. But an approximate value of pi is 22/7
Positive: 33.333333333333 %
Answer #28 | 24/04 2015 20:56 Pi fraction= 22/7
Positive: 33.333333333333 %
Answer #29 | 21/04 2015 03:02 pi (π) is an irrational number. It can't be represented as the ratio of integers. You can express pi as the ratio of the circumference to the diameter, so: π = circumference / diameter But those can't both be integers. There are several ways to approximate pi. One common one is 22/7, but it is only accurate to 2 decimal places. π ≈ 3.141592653589793238...
Positive: 33.333333333333 %
Answer #30 | 21/04 2015 22:38 Pi is a transcendental number, so it cannot be expressed using algebraic numbers.
Positive: 33.333333333333 %
Answer #31 | 23/04 2015 14:06 I like el atlatl. He likes Pi too.
Positive: 33.333333333333 %
Answer #32 | 21/04 2015 15:38 Pi is a transcendental number, so it cannot be expressed using algebraic numbers.
Positive: 33.333333333333 %
Answer #33 | 24/04 2015 13:56 Pi fraction= 22/7
Positive: 33.333333333333 %
Answer #34 | 22/04 2015 14:01 There are no two integers such that π = a/b. 22/7 is a reasonable approximation, π can be expressed with greater precision by more complex fractions. One of the best is 355/113, only off by 3 in the 8th place. That's an error of only one part in 10 million! There is no better approximation with a denominator less than 30,000. Still. it seems to me that it's just as easy to remember 3.1415926.....
Positive: 33.333333333333 %
Answer #35 | 26/04 2015 21:52 about 22/7, which is more accurate than 3.14 but the most accurate way to get pi is to use the pi symbol.
Positive: 33.333333333333 %
Answer #36 | 26/04 2015 16:36 Approximitly 22/7
Positive: 33.333333333333 %
Answer #37 | 20/04 2015 20:02 π = π/1 and π/1 is a fraction. However π does NOT equal a/b for any integers a and b. So, although π is a perfectly good real number, like most real numbers it is irrational.
Positive: 33.333333333333 %
Answer #38 | 26/04 2015 15:03 cannot be expressed as a fraction
Positive: 33.333333333333 %
Answer #39 | 24/04 2015 05:42 355/113 is a very good approximation of pi (better than 22/7 by 4 digit places), and very easy to remember too! just look at it as 113/355, but reversed.
Positive: 33.333333333333 %
Answer #40 | 20/04 2015 22:57 As Jeff, Puzzling, Rita, and freond1 have said, it is irrational, and so, not equal to any fraction (i.e., ratio of integers). However, like all irrational numbers, it is the limit of some infinite sequence of rational numbers (fractions). The technique of continued fractions (CF) can be used to produce the "most efficient" such sequence. The usual practice in CFs is to keep all the terms positive, so that any positive integer can appear in it. It is more efficient, for approximation purposes, to allow the terms to have either sign, but restrict them to having absolute value ≥ 2, with the further stipulation that, following any term of ±2, must be a term of the same sign. What are CFs? They are compound fractions that just keep going, usually with all numerators = 1, where you just keep adding a new (reciprocal) fraction to the latest denominator. They are often written as: a+1/b+1/c+1/d+ . . . — meaning: a+1/(b+1/(c+1/(d+ . . . ))) and then the sequence of terms is often written as: [a; b, c, d, . . .] When you truncate the CF at some finite point, you can simplify the resulting finite compound fraction: a/1, (ab+1)/b, (abc+a+c)/(bc+1), . . . For π, the first 10 terms of the sequence are: [3; 7, 16, -294, 3, -4, 5, -15, -3, 2, . . .] the corresponding fractions (obtained by simplifying the compound fractions & taking absolute values) being: 3 / 1 22 / 7 355 / 113 104348 / 33215 312689 / 99532 1146408 / 364913 5419351 / 1725033 80143857 / 25510582 245850922 / 78256779 411557987 / 131002976 . . . Note: The magnitude of the first *omitted* term is a fair measure of the efficiency of the resulting fraction. There is, AFAIK, no easy way to generate these terms for π, but there are other CFs, with non-unit numerators, that do follow a predictable pattern (see Source).
Positive: 33.333333333333 %
Answer #41 | 26/04 2015 14:11 we know 1 + x + x^2 + x^3..... = 1/1-x replace x by -x^2 1 - x^2 + x^4 - x^6 = 1/1+x^2 integrate both sides x - x^3/3 +x^5/5 - x^7/7..... = tan^-1(x) put x=1 1 - 1/3 + 1/5 .....= pi/4 so pi = 4/1 - 4/3 + 4/5 - 4/7 ...
Positive: 33.333333333333 %
Answer #42 | 22/04 2015 15:02 Pi is an irrational number and cannot be written as a fraction. There are fractons close to pi, however, like 22/7 and 355/113.
Positive: 33.333333333333 %
Answer #43 | 22/04 2015 22:02 Pi is an irrational number and cannot be written as a fraction. There are fractons close to pi, however, like 22/7 and 355/113.
Positive: 25 %
Answer #44 | 26/04 2015 14:09 there's no exact fractional value for pi but the closest and most common value is 22/7
Positive: 0 %
Answer #45 | 22/04 2015 21:01 There are no two integers such that π = a/b. 22/7 is a reasonable approximation, π can be expressed with greater precision by more complex fractions. One of the best is 355/113, only off by 3 in the 8th place. That's an error of only one part in 10 million! There is no better approximation with a denominator less than 30,000. Still. it seems to me that it's just as easy to remember 3.1415926.....
Positive: 0 %
Answer #46 | 26/04 2015 10:11 The idiot who said pi is a rational number doesn't know what he's talking about. Pi IS irrational because it cannot be expressed as the ratio of two integers. This is a very well-known fact about Pi. It has an infinite number of digits at the end. 22/7 is a decent approximation, but it is not exact. There is no answer to your question. Pi is irrational, and therefore cannot be expressed as a fraction.
Positive: 0 %
Answer #47 | 26/04 2015 22:03 cannot be expressed as a fraction
Positive: 0 %
Answer #48 | 24/04 2015 05:00 impossible to do
Positive: 0 %
Answer #49 | 23/04 2015 17:01 there is no exact fraction to represent pi, but a close fraction to pi would be 22/7
Positive: 0 %
Answer #50 | 26/04 2015 21:09 there's no exact fractional value for pi but the closest and most common value is 22/7
Positive: 0 % 