The symbol r represents the radius of a circle. Explain why C = • 2r is a valid formula for the circumference of a circle.
Problem A8
An irrational number cannot be written as a quotient of any two whole numbers. Yet we sometimes see written as 22/7 or 3.14. Explain what the reason for this may be.
Problem A9
Since is an irrational number, can both the circumference and the diameter be rational numbers? Can one of them be rational? Explain using examples.
Problem A10
When mathematicians are asked to determine the circumference of a circle, say with a diameter of 4 cm, they often write the following:
C = • d = • 4
In other words, the circumference of the circle is 4 cm. Why do you think they record the answer in this manner? Why not use the key on the calculator to find a numerical value for the circumference?
Is the value for given on a calculator an approximation or an exact amount? Close Tip
Note that we have worked with two forms of the standard equation that shows the relationship between circumference and diameter:
C = • d = C/d
Since is an irrational number, the exact circumference can only be expressed using the symbol for . Sometimes, however, we want to solve a real problem and find an approximate value for a circumference. In that case, we must use one of the approximations for . Inexactness may also occur when determining a numerical value for circumference (or diameter) because of measurement error.
given on a calculator an approximation or an exact amount? 