Zoom Test Course

The last set we need for our number sets is the set of real numbers, . This includes all the
previous sets and also the irrational numbers. Irrational numbers are numbers which cannot
be written as fractions (or ratios) made up of one integer over another.

The Greek letter π (which is spelled and pronounced as pi) is used to represent what is
perhaps the most famous irrational number. Pi is the number you get when you divide the
length of the circumference of a circle by its diameter. You can never find the value of π exactly.
We will do some experiments later in the course to see how close we can get to the calculated
value of π.

Irrational numbers include square roots of numbers that are not perfect squares themselves,
and as we find in the case of π, irrational numbers are decimals that go on and on forever,
and never repeat any pattern.

The number π (= 3.1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 …) has been calculated to
billions of places of decimal by high-powered computers, using a more advanced method
than measuring the circumference and diameter of a circle. However, no recurring pattern has
been found.

Recurring decimals are not irrational numbers because they can always be written as fractions.
For example, 0.666 666 666 66… = 23
, and 0.285 714 285 714 285 714… = 2
7.
Recurring decimals do, of course, have a repeating pattern, unlike irrational numbers.
Write down the sequence of numbers that recur in the decimal equivalent of 2
7.
Figure 1.2 will help you to see how these sets of numbers build up.
Each number type has been drawn with two or three examples in it.
Another way to show these sets is on number lines like in Figure 1.3. Some examples of each
set are shown below. The arrows show that the sets go on forever in that direction.