Download Section 2.1

Mr. Borosky
Section 2.1
2.1 Use Integers and Rational Numbers p. 64-70
Algebra 1
Objective: 1. You will graph and compare positive and negative
numbers.
Whole Numbers – the set of numbers {0, 1, 2, 3, ...}
Natural Numbers – the set of numbers {1, 2, 3, ...}
Integers – the set of numbers {... -3, -2, -1, 0, 1, 2, 3, ...}
Positive Integers – integers greater than 0 {1, 2, 3, ...}
Negative Integers – integers less than 0 {... -3, -2, -1}
ZERO is neither negative or positive
See graph of the Number Line p. 64
Rational Number - Numbers that are the result of dividing an integer
a
by a nonzero integer. It can be written as a fraction
where a and
b
b are integers and b ≠ 0.
Real Numbers – the set of numbers consisting of all the Rational and
Irrational numbers.
Irrational Number – anything that is not rational. It cannot be
written as a fraction. They are non-terminating and non-repeating.
Examples, Square Roots of non perfect squares and Π ( 7 , Π)
Terminating Decimals – a decimal numeral in which, after a finite
number of decimal places, all succeeding place values are 0, as 1/8 =
0.125.
Repeating Decimals – It has a block of digits that repeats
indefinitely (this block may have any amount of digits and may or
may not start right after the decimal point). The horizontal bar
over the numbers indicates the repeated part, example 2.317.
Non-repeating Decimals – a decimal representation of any irrational
number, having the property that no sequence of digits is repeated.
Opposites (Additive Inverse) – numbers that are the same distance
from the origin but on opposite sides of the origin. Ex. The
opposite of -3 is 3, The opposite of 5 is -5, the opposite of 0 is 0
Note: you read the expression
“-a”
as the opposite of a
2.1 Use Integers and Rational Numbers p. 64-70
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Mr. Borosky
Section 2.1
Algebra 1
Absolute Value – the distance between a number and zero on the
number line. It is denoted with vertical bars |x|.
Key Concept Box p. 66 Absolute Value
If a is positive then |a| = a
Example |2| = 2
If a is 0 then |a| = 0
Example |0| = 0
If a is negative then |a| = -a
The opposite of a
Example |-2| = -(-2) = 2
The absolute value of any number except zero is positive and the
absolute value of 0 is 0.
Conditional Statement – has a hypothesis and a conclusion.
If-Then Statement – is a form of a conditional statement.
Hypothesis – is the IF part of the conditional statement
Conclusion – is the THEN part of the conditional statement
Counterexample – an example that makes the conclusion False when the
hypothesis is satisfied.
2.1 Use Integers and Rational Numbers p. 64-70
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