1. 3.2
Rational Numbers

2. Rational Number
Any number that can be written in the form of a fraction.
a and b have to be integers

3. Write Each Number as a Rational Number
aka a Fraction

4. Write Each Number as a Rational Number
aka a fraction
tens
ones .
tenths
hundredths
thousandths
Ten - thousandths

5. Writing Decimals as Fractions Let me first introduce the shortcut
How do you write a repeating decimal into a fraction?
Let me first introduce the shortcut
IF and ONLY IF the bar notation is COMPLETELY over ALL of the numbers after the decimal, you can use this shortcut.
DISCUSS: Do you notice a pattern?
Put all of the digits under bar notation in a fraction with the equal number of 9’s

6. Writing Decimals as Fractions
Now for the rationale
Let’s use algebra to find the fraction of
Let’s assign a variable
Multiply both sides by 100
Subtract both sides by n
Substitute
Simplify
Divide both sides by 99

7. Examples
Write each decimal as a fraction in simplest form. A) B) C)

8. Rational Vs. Irrational
Terminating or repeating decimals
Decimals that do not terminate or repeat Pi

9. Identify all Sets to which each number belongs
a.) 0 Whole, Integer, Rational b.) … Irrational c.) 1.45 Rational d.) -4 Integer, Rational

10. Homework
CA Math Page 104 (12-48) even