Download Section 1.1 The Real Number System Classify each of the numbers

Section 1.1 The Real Number System
Classify each of the numbers in the set
1
3
{−4.2, − 9 , 0, 11 , √4, √11, 5. 5̅, 5.543}
Natural:
Integers:
Rational:
Irrational:
Classify each of the numbers in the set
Natural:
Integers:
Rational:
Irrational:
Section 1.1 The Real Number System
The Real Number Line
Ordering Real Numbers
1
10
Plot the following points on the real number line: 0.5, −2.6, − 3 , − 3 , √5
Which is the smallest number? _____________
How do you know? ______________________________________________________
Write an inequality representing the relationship of the four values above: ________________________
Distance on the Real Number Line
Plot the numbers -8 and 7 on the real number line below
Use the number line to find the distance between the two real numbers __________________
Use an inequality symbol to represent the relationship of the two real numbers _________________
Use the formula in the box above to verify this distance ________________________________
7
1
Plot the numbers − 4 and − 2 on the real number line below
Use the number line to find the distance between the two real numbers __________________
Use an inequality symbol to represent the relationship of the two real numbers _________________
Use the formula in the box above to verify this distance ________________________________
Section 1.1 The Real Number System
Opposites (Additive Inverses) and Absolute Value
Two real numbers are called __________________ if they lie the same distance from, but on opposite
sides of, 0 on the real numbers line.
The opposite of 2 is __________.
The opposite of a negative number is called a __________________ . The opposite of -2 is ___________
Opposite numbers are also known as ___________________ because their sum is 0 ( __ + ___ = 0 )
The distance between a real number a and 0 (the origin) is called the ________________________ and
is denoted by ______ .
|5| = the distance between ___ and ___ = ___
|−8| = the distance between ___ and ___ = ___
If 𝑎 is a real number:
|𝑎| = 𝑎 if _________
|𝑎| = - 𝑎 if ________
Evaluate: |. 6| = _____
|−3| = _____
−|−7| = _____
Place the correct inequality symbol (< , > or =) between each pair of real numbers
|−9| ____ −9
2 ____ −|−2|
−|−3| _____ −2
For each of the problems below, find two possible values for 𝑎
The distance between 𝑎 and 3 is 5 ________
The distance between 𝑎 and -1 is 6 ________
Inequality Notation Write the following statements using inequality notation:
𝑥 𝑖𝑠 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 ________
𝑢 𝑖𝑠 𝑎𝑡 𝑙𝑒𝑎𝑠𝑡 16 __________
𝑥 𝑖𝑠 𝑛𝑜𝑛𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒 _________
A bicycler’s race speed s is at least 16 miles per hour and at most 28 miles per hour _________________