1. Rational Numbers
Math 8

2. OBJECTIVE: -You will be able to identify rational numbers
-You will be able to write fractions as decimals
Word Watch:
-rational number
-terminating decimals
-repeating decimals

3. PICK YOUR BRAIN!! What is a whole number? What is an integer?
Positive whole numbers starting with 0.
Ex: 0,1,2,3,4, etc.
What is an integer?
The numbers …, -4, -3, -2, -1, 0, 1, 2, 3, 4…
Consists of negative #’s, zero, & positive #’s.

4. (In other words, it can be written as a fraction.)
A rational number is a number that can be written as where a and b are integers.
(In other words, it can be written as a fraction.)
Let’s look at the relationship among whole numbers, integers, and rational numbers. a b

5. Rational #’s Integers Whole #’s _ 0.8 -6 2 -10 13 8 -4 49 1 12 5 -1.442
-10 13 8 -4 49 1 12 2 3 5 _
-1.44
5.2

6. Identify Rational Numbers
Show that the number is rational by writing it as a fraction.
a) 6 b)
c) 0.75 d) 6 1 = 3 5 -3 5 = - 75
100 3 4 = = 1 3 -7 3 -2 =

7.  YOUR TURN!! 
Show that each number is rational by writing it in form.
a) 2.5
b) -1
c) -0.8 d) a b 5 2 = -1 1 = -8 10 -4 5 = = 5 8 5 8 =

8. Writing Fractions as Decimals7 20
Write as a decimal . 3 5
______
Write zeros in dividend
as placeholders.
20)7.00 60
____
100
100
remainder is zero

9. Write 3 as a decimal What can you tell me about the 3?5 8
Write 3 as a decimal
What can you tell me about the 3?
3 is a whole number. It will be on the
left side of the decimal point. 0. 6 2 5
______
8)5.000 48 20 16 40 40
= 3.625

10.  YOUR TURN 
Write as a decimal
Write as a decimal 3 10
0.3 4 5
3.8

11. VOCAB
When a long division problem results in a remainder of 0, the quotient is a terminating decimal.
Repeating decimal: where one of more digits repeat without end. Can be written with a bar over the digit(s) that repeat. (bar notation)

12. Writing Fractions as Repeating Decimals5 3
Write as a decimal 1. 6 6 6
______
The digit 6 keeps repeating!
3)5.000 3 20 18 20 18
The remainder will never be zero 20 _ 5 3
= 1.6

13. Write as a decimal 13 33  The digits 3 and 9 keep repeating 0. 3 9 3
_________
33)13.000 99
310
297
130 99
 Remainder will never be zero
310

14.  YOUR TURN  7 9
Write as a decimal __
0.7