a Circle perimeter as expression of $\pi$ Conflict? I know that the the perimeter of a circle is 
$$2\pi r$$
The problem is that $\pi$ is un-finite number. ( its decimal representation never ends)
Im having trouble to understand  : 
If I "cut" the circle  and make it as a line :  - and i look at this line : 
the line has a finite length ! ( its length is NOt infinite !)
but it cant be since - it has an un-finite number  inside it ( $2\pi r$)..... ( the $\pi$)
how can a line length is not infinite - but it has an un-finite number inside it...
can you please explain ?
 A: The number $\pi$ is perfectly finite. It is just as finite as $4$, and indeed it is less than $4$. Drawing the the square of side $2$ that just contains the circle with radius $1$ shows that. The  decimal representation of $\pi$ is non-terminating.  There are plenty of numbers with a non-terminating decimal expansion that are a good deal more familiar than $\pi$. One example is $\frac{1}{3}$.
The decimal expansion of $\frac{1}{3}$, however, is periodic. If you want a number somewhat less mysterious than $\pi$ with a non-periodic decimal expansion, look at $\sqrt{2}$. This number represents the length of the diagonal of a square of side $1$.  I expect that you do not think of the the length of that diagonal, or of the number $\sqrt{2}$, as infinite. 
The arithmetic of rational numbers, that is, numbers of the form $\frac{a}{b}$, where $a$ and $b$ are integers, is, through long years of practice, familiar to almost everyone.  There are some technical hurdles in dealing with the arithmetic of irrational numbers, but these were overcome a long time ago.
A: Think about this, $\pi<4$. Now suppose you have a circle with radius $r=1$. Plug into your equation, 
perimeter$=2\times pi\times r<2*4*1=8$ and 8 is a finite number. 
You can also bound your perimeter from below, since $3<\pi$, then 
perimeter$=2\times pi\times r<2*3*1=6$. 
So for this particular circle of radius 1, your perimeter is between 6 and 8. 
you might not be able to express the exact value of the perimeter in fractions, but that does not mean that the perimeter is infinite. For example, $1/5$ is the representation of the infinite number $.2\bar{0}$ and this value is definitely finite.
A: Let $r=1/2\pi$, then the circle has perimeter 1=1.0000000... And the radius which is a finite straight line has a non-repeating infinite decimal expansion.
