3.2

Rational Numbers

Rational Number

• Any number that can be written in the form of a fraction.

a

b

a and b have to be integers

0b

Write Each Number as a Rational Number

aka a Fraction

1.)66

a

37

6

.) 12b

12

1

Write Each Number as a Rational Number

aka a fraction

tens ones . tenths hundredths thousandths Ten - thousandths

.)0.84c84

100

21

25

.)5.875d875

51000758

How do you write a repeating decimal into a fraction?Writing Decimals as Fractions

Let me first introduce the shortcutIF and ONLY IF the bar notation is

COMPLETELY over ALL of the numbers after the decimal, you can use this shortcut.

9

88.0

99

1717.0

9999

50055005.0

DISCUSS: Do you notice a pattern?

Put all of the digits under bar notation in a fraction with the equal number of 9’s

Writing Decimals as FractionsNow for the rationale

17.0Let’s use algebra to find the fraction of

Let’s assign a variable 17.0n

Multiply both sides by 100 17.17100 nSubtract both sides by n nnn 17.17100

Substitute 17.017.17100 nn17.0n

Simplify 1799 n

Divide both sides by 99 99

17n

Examples

3.0

Write each decimal as a fraction in simplest form.

A)

54.0B)

213.0C)

9

3

3

1

99

54

11

6

999

213

333

71

Rational Vs. Irrational

Rational• Terminating or repeating

decimals

Irrational• Decimals that do not

terminate or repeat• Pi

Identify all Sets to which each number belongs

a.) 0Whole, Integer, Rationalb.) 1.313313331…Irrationalc.) 1.45Rationald.) -4Integer, Rational

4.)15

e rational

Homework

CA Math Page 104 (12-48) even