Page 160 - ABCTE Study Guide_Neat

The above diagram shows the relationships among the following types of numbers: real
numbers, rational numbers, irrational numbers, whole numbers, and integers. For example,
every type of number in the diagram is a real number. Moving in, all integers and whole numbers are
rational numbers and, subsequently, all whole numbers are integers. And, as you move out from the
center of the diagram, the same rule holds true. Every whole number is an integer, and every integer is a
rational number .

Many numbers fit into several sets of numbers. Think about putting the number into its most restrictive set
in the diagram above, and then you’ll be able to see how a number can exist in more than one set.

For example, –7 is a real number, rational number, and integer, but it is not a whole number because it is
negative.

What categories does fit into? You should be thinking irrational number and real number.

How about ? Since the square root of 9 is 3, it fits into the categories of real number, rational number,
integer, and whole number.

Try this one on your own:

Question

Choose the correct statement below:

A No rational numbers are integers.

B All rational numbers are real numbers.

C No irrational numbers are real numbers.

D All integers are whole numbers.