Neil and Sandy are cutting out circles as decorations. Sandy comments that the distance around a circle is always a rational number. True or False?

Question

this is for algebra 2

Answer 1

     The distance around a circle is called the circumference and can be calculated using the formula C= pi*d or C= 2*pi*r, d is the diameter and r is the radius. Since both of these formulas involve pi and pi is an irrational number, the circumference is also an irrational number. So Sandy is wrong.

Answer 2

the distance around a circle is its circumference

circumference=pi*diameter

pi is an irrational number and let the diameter be a rational number

an irrational number times a rational number gives you an irrational number

you may think it's a rational number because you use a rational approximation for pi

you can use 3.14, 3.14159265, 3.1416, 22/7, etc, and these numbers are rational numbers but again they are only approximations for the true value of pi which is a non-ending, non-repeating decimal, an irrational number