For the PI value 22/7 in radians what that numerator 22 and denominator 7 represents ?

Question

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Answer 1

The mathematical constant π is an irrational real number, approximately equal to 3.14159, which is the ratio of a circle's circumference to its diameter in Euclidean geometry.
The rational number 22⁄7 is a widely used Diophantine approximation of π. It is a convergent in the simple continued fraction expansion of π. It is greater than π, as can be readily seen in the decimal expansions of these values:

π=3.141592..........
22/7=3.142857.....

(Archimedes of Syracuse discovered, by considering the perimeters of 96-sided polygons inscribing a circle and inscribed by it, that π is between 223⁄71 and 22⁄7. The average of these two values is roughly 3.1419.)

Answer 2

22/7 for 'pi' is highly approximate. Even in your calculator the error between the two is 0.0004025. I give here another (better) ratio = 355/113 that gives an accuracy of 0.0000 00085. There can be any number of such ratios and there are computer programs and more to spit out decimal values as a recursive process. Decimal notation of expressing a number has been accepted as a standard method in preference to, say fraction form. But decimal form has a tendency to run into infinite number of places for even numbers like 1/3, 1/7 etc. Howeever when expressed in any form a number is also an algorithm or rule of computation. Viewed in that light 'pi' can be called as 4 Tan^(-1) 1. The fact is, this number 'pi' is absolutely irrational. May be more than any other number if only there is a 'measure of irrationality' like that of Randomness. I reproduce here my favourite (of many others too)expression that has 5 of the most mathematically used numbers: exp{i pi}+1=0. The numbers are: 0, 1, i, e & pi.

Answer 3

The PI value is the ratio of circumference of a circle to the diameter of the circle.
So the 22 represents the circumference and 7 represent the diameter.

Answer 4

Every irrational number has a unique development under the form x=a+1/{b+1/{c+1/{d+1{.......}}}}, where a,b,c,d,... are integers. This is called a continued fraction. When you stop after a few steps you get the bast approximation for a given range of denominator. For pi you have a=3 and b=7 and that gives you 3+1/7. The next approximation which is much better is 355/113, and comes from c=... I let you work it out.

Answer 5

In a circle with a diameter 7 units the circumference will be 22 units

Answer 6

pi is an irrational number i.e. it is a non terminating decimal. its value is

3.14158265358879.........................

22/7 represents pi correct to 2 places of decimals. since we do not need much accuracy in most of the calculations, we use this value.

355/113 is also a representation of pi which is more accurate

Answer 7

22/7 is only an approximation of PI. 22/7 is used very frequently because its value is very close to the actual value of PI i.e. 3.14159 truncated to 5 decimal places.

Answer 8

PI IS CONSTANT WHOSE VALUE IS DERIVED AFTER DIVIDING THE CIRCUMFERNCE BY IT'S DIAMETER.THE REAL VALUE OF PI IS 3.14......IT IS A IRRATIONAL NUMBER ,i.e,IT IS NEITHER TERMINATING NOR RECCURRING .FOR THE SIMPLICITY OF OUR'S MODERN MATHEMATICIANS HAVE TAKEN THE VALUE OF PI AS 22/7.REMEMBER THE VALUE OF PI IS ALWAYS CONSTANT NO MATTER WHAT THE CIRCUMFERENCE AND DIAMETER IS

Answer 9

Long before the Y-ANSWERS existed Archimedes used a theorem by Euclid to find limits for Pi.
See for example: http://itech.fgcu.edu/faculty/clindsey/mhf4404/archimedes/archimedes.html

Answer 10

22/7 is just the closest value you can get to PI if you were to express it by integer/integer