1. Making Sense of Rational and Irrational Numbers
Objectives: Identify number sets.
Write decimals as fractions.
Write fractions as decimals.

2. The set of real numbers is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers.
Irrational numbers
Rational numbers
Real Numbers
Integers
Whole
numbers

3. Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals.
4 5 23
3 = 3.8
= 0.6
1.44 = 1.2

4. Rational Numbers Natural Numbers - Natural counting numbers.
1, 2, 3, 4 …
Whole Numbers -
Natural counting numbers and zero.
0, 1, 2, 3 …
Integers -
Whole numbers and their opposites.
… -3, -2, -1, 0, 1, 2, 3 …
Rational Numbers -
Integers, fractions, and decimals.
Ex:
-0.76, -6/13, 0.08, 2/3

5. Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so is irrational.
A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Caution!

6. Identify each root as rational or irrational.

7. Decimal to Fraction: A skill you will need for this unit!
To change a decimal to a fraction by dividing the denominator by the numerator
5/10= 5 ÷ 10 = 0.5

8. Complete the table.
Fraction
Decimal

9. Rational and Irrational Numbers
Determine whether the following are rational or irrational.
(a) (b) (c) 0.666… (d) (e)
rational
irrational
rational
rational
irrational
(f)
irrational

11. RULES FOR ADDING AND MULTIPLYING RATIONAL AND IRRATIONAL NUMBERS
Rule 1: Rational + Rational = Rational
Example:
Rule 2: Rational x Rational = Rational
Example:
Rule 3: Rational x Irrational = Irrational
Example:

12. RULES FOR ADDING AND MULTIPLYING RATIONAL AND IRRATIONAL NUMBERS
Rule 4: Irrational + Rational = Irrational
Example: