Algebra 2-1 Rational Numbers on a Number Line A number line can be used to show the sets of natural numbers, whole numbers and integers. Values greater than 0, or positive numbers, are listed to the right of 0, and values less than 0, or negative numbers, are listed to the left of 0. Harbour

Algebra 2-1 Rational Numbers on a Number Line Integers Whole Numbers Natural Numbers – 4 – 3 – 2 – 1 0 1 2 3 4 | | | | | | | | | Negative numbers Positive numbers Zero is neither negative nor positive Harbour

Algebra 2-1 Rational Numbers on a Number Line Another set of numbers you can display on a number line is the set of rational numbers. A rational number is any number that can be written in the form , where a and b are integers and b ≠ 0. Some examples of rational numbers: Harbour

Algebra 2-1 Rational Numbers on a Number Line A rational number can also be expressed as a decimal that terminates or as a decimal that repeats indefinitely: = = = = = = = Harbour

Algebra 2-1 Rational Numbers on a Number Line Obtain and secure this handout in your notes! Harbour

Algebra 2-1 Rational Numbers on a Number Line To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line. The number that corresponds to a point on a number line is called the coordinate of that point. Harbour

Identify Coordinates on a Number Line Name the coordinates of the points graphed on the number line. The dots indicate each point on the graph. Answer: The coordinates are {–9, –7, –6, –3}. Example 1-1a

Graph Numbers on a Number Line Answer: Example 1-2a

Graph Numbers on a Number Line Answer: Example 1-2b

Graph Numbers on a Number Line Graph each set of numbers. a. {–5, 2, 3, 5} b. Answer: Answer: Example 1-2d

Algebra 2-1 Rational Numbers on a Number Line On the number line, notice that –4 and 4 are on opposite sides of zero and they are the same distance from zero. In mathematics, we say they have the same absolute value, 4. – 4 – 3 – 2 – 1 0 1 2 3 4 | | | | | | | | | Harbour

Algebra 2-1 Rational Numbers on a Number Line The absolute value of a number n is the distance the number is from zero on the number line and is written | n |. The absolute value of a number is always greater than or equal to zero. Harbour

Absolute Values of Rational Numbers Find . unit from 0 in the negative direction. Answer: Absolute Values of Rational Numbers Find . 0.25 is 0.25 unit from 0 in the positive direction. Answer: Example 1-3a

Absolute Values of Rational Numbers Find each absolute value. a. b. Answer: Answer: 6.3 Example 1-3c