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?

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.