rational numbers on a number line a number line can be used to show the sets of natural numbers,...
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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.
Rational Numbers on a Number Line
– 4 – 3 – 2 – 1 0 1 2 3 4
| | | | | | | | |
Negative numbers Positive numbers
Zero is neither negative nor positive
Natural Numbers
Whole Numbers
Integers
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.
b
a
Some examples of rational numbers:
2
1
3
25
17
3
15
11
14
1
3
99
265
Rational Numbers on a Number Line
5.0
A rational number can also be expressed as a decimal that terminates or as a decimal that repeats indefinitely:
2
1
3
25
17
3
15
11
14
1
3
3.0 4.3 5 27.1 3 ...676767.2
99
265
= ======
Rational Numbers on a Number Line
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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.
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}.
Identify Coordinates on a Number Line
Graph .
Answer:
Graph Numbers on a Number Line
Graph {–1.5, 0, 1.5, …}.
Answer:
Graph Numbers on a Number Line
Graph each set of numbers.
a. {–5, 2, 3, 5}
b.
Answer:
Answer:
Graph Numbers on a Number Line
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 | | | | | | | | |
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.
Find .
unit from 0 in the negative direction.
Answer:
Absolute Values of Rational Numbers
0.25 is 0.25 unit from 0 in the positive direction.
Answer:
Find .
Absolute Values of Rational Numbers
Find each absolute value.
a.
b.
Answer:
Answer: 6.3
Absolute Values of Rational Numbers