Download 1-3: Exploring Real Numbers

1 - 3: Exploring Real Numbers
Objectives:
• You will be able to classify numbers as subsets of real numbers.
• You will be able to compare numbers by size.
• You will be able to determine the absolute value of a number.
Definition:
line
number
A real number is any number that lies on the _______________ ___________.
fraction
A real number is any number that can be expressed as a ____________________.
Examples:
Real numbers include: ______________________________________________
Practice Problems:
1. Name the set(s) of numbers to which each number belongs:
­ 12
­ 4.67
0
5
12
2. Which set of numbers is most reasonable for each situation?
a. the number of students who will go on a class trip
b. the height of the door frame in your classroom
c. the most reasonable cost for a video game
Counter­Examples:
false
example
Any ___________ that proves a statement ______________ is a counter­example.
one
In order to prove a statement false, you need only __________ counter­example.
Practice Problems:
3. Determine if the given statement is true or false. If it is false, provide at least one counter­example.
a. all whole numbers are integers
b. no fractions are whole numbers
Extra Problems (not in your notes):
Decide whether each statement is true or false.
If the statement is false, give a counterexample.
. Every whole number is an integer.
. Every rational number is a real number.
. Every integer is a whole number.
. Every multiple of 7 is odd.
Definition:
order
To ______________ numbers, you will need to compare the values of the numbers.
decimals
The values of numbers can be done by comparing their ____________________ or
fractions
their __________________ (with common denominators).
inequality
An ________________________ is a mathematical sentence that compares the >
<
≥
≤
values of expressions using symbols such as _____ , _____ , _____ , or _____.
Helpful Hint:
When ordering numbers, it sometimes helps to place the values along a number line then put in the inequalities.
Practice Problems:
Use decimals and a number line to order the following fractions from least to greatest.
** With problems like these, be sure to read them carefully. **
** The question could be asking for least to greatest or greatest to least. **
Order the following from least to greatest:
Definitions:
absolute
value
The ____________________ ______________ of a number is its | |
distance from 0 on a number line. The symbol used for it is _______.
Two numbers that are the same distance from 0 on a number line, but lie in opposites
opposite directions (one + and one ­) are called __________________.
equal
The absolute value of opposites are ______________.
Example:
Use the number line to find | 3 | and | ­ 3 |.
­5
­4
­3
­2
­1
Practice Problems:
Find the absolute value of each.
0
1
2
3
4
5
1-8: Properties of Real Numbers
Objectives:
• You will be able to identify the properties of real numbers.