1. UNIT 1
Chapter 1-1
Number Systems

2. Vocabulary
A number line – is used to show a set of natural numbers, whole numbers, and integers
Positive Numbers – to the right side of zero
Negative Numbers – to the left side of zero -4 -3 -2 -1 1 2 3 4
Negative Numbers
Positive Numbers

3. Vocabulary Real Numbers: Include Rational and Irrational Numbers
Natural Numbers: 1, 2, 3…
Whole Numbers: 0, 1, 2, 3, 4…
Integers: -3, -2, -1, 0, 1, 2, 3…
Rational Numbers: Any ordinary number in arithmetic. Any number that you can write as a quotient in 𝐴 𝐵 of two integers where, b ≠ 0.
Examples: 1, -6, 5.8, .227, −3 4
Irrational Numbers: Numbers that cannot be expressed as terminating or repeating decimals, or in the form of 𝐴 𝐵 , where a and b are integers and b≠ 0

4. Real Numbers Rational Numbers Integers Irrational Numbers
Whole Numbers
Natural Numbers
Irrational Numbers

5. Number Systems Real Numbers Rational Numbers Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Irrational Numbers

6. From least to greatest =
Examples
1) Write two lists of fractions equivalent to 𝟏 𝟐
List 1: Positive numerator and denominator
1 2 = 2 4 = 3 6 = …
List 2: Negative numerator and denominator
1 2 = −2 −4 = −3 −6 =…
2) Put each rational number from least to greatest
.25, 𝟑 𝟒 , -.2, 3
From least to greatest =
-.2, .25, 3 4 , 3

7. Let’s Try Some Examples
Name the set (s) of numbers to which each real number belongs
) ) √7
List three fractions equivalent to each fraction
4) ) −5 6
List each rational number from least to greatest
5) 1 4 , 3, -2, ) 1, -4, −10 10

8. Let’s Check Our Answers
Name the set (s) of numbers to which each real number belongs
) ) √7
Natural Number, Rational Irrational
Whole Number,
Integer, Rational Number
List three fractions equivalent to each fraction
4) ) −5 6
= 𝟐 𝟐𝟎 = 𝟑 𝟑𝟎 = 𝟒 𝟒𝟎 = −𝟏𝟎 𝟏𝟐 = −𝟏𝟓 𝟏𝟖 = −𝟐𝟓 𝟑𝟎
List each rational number from least to greatest
5) 1 4 , 3, -2, ) 1, -4, −10 10
= -.2, -2, 1 4 , = -4, − , 1