The real number system consists of two kinds of numbers: rational numbers and irrational numbers. Rational numbers include integers like counting numbers, whole numbers, and their opposites, as well as fractions that can be written as a ratio of two integers. Irrational numbers are any real numbers that cannot be expressed as a ratio of integers, and are therefore non-repeating and non-terminating decimals like pi.

2. REAL NUMBERS Two Kinds of Real Number
The real number system consists of rational and irrational numbers.
Rational Numbers
Irrational Numbers

3. REAL NUMBERS Rational Numbers
Rational Numbers
Natural numbers, whole numbers, and integers are all rational numbers.

4. Examples of Rational Numbers
REAL NUMBERS
Natural numbers are the natural numbers.
{1, 2, 3, 4, 5, 6, …}
Whole numbers consist of the counting numbers and zero.
{0, 1, 2, 3, 4, 5, …}
Integers consist of the counting numbers, their opposites
(negatives), and zero.
{…, -3, -2, -1, 0, 1, 2, 3, …}
Rational Number is a real number that can be written as a simple
fraction
2 3
7 5.25
1
3
0.6 -9.261
A repeating decimal continues the same digit or block of digits forever.

5. REAL NUMBERS Examples of Rational Numbers

6. REAL NUMBERS What is an irrational number?
Irrational Numbers
are numbers that cannot be written as a ratio of two integers.
Irrational numbers are non-repeating and non-terminating decimals
because the decimal form of the number never ends and never repeats.
The most common irrational number is pi (п).
The value of п is 3.141592654…

7. REAL NUMBERS QUIZ
Tell whether each real number is rational or irrational.
-23.75 rational decimal terminates
4.750918362… irrational decimal does not terminate
5
9
rational number is in fraction form
√15 irrational decimal form does not terminate

8. REAL NUMBERS Review