Evaluating Algebraic Expressions 4-8 The Real Numbers Rational and Irrational Numbers.
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Evaluating Algebraic Expressions 4-8 The Real Numbers Rational and Irrational Numbers
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Transcript of Evaluating Algebraic Expressions 4-8 The Real Numbers Rational and Irrational Numbers.
Evaluating Algebraic Expressions
4-8 The Real Numbers
Rational and Irrational Numbers
Evaluating Algebraic Expressions
4-8 The Real Numbers
How do I distinguish between How do I distinguish between rational and irrational rational and irrational
numbers?numbers?
Rational and Rational and Irrational Numbers Irrational Numbers Essential QuestionEssential Question
Evaluating Algebraic Expressions
4-8 The Real Numbers
real numberirrational number
Vocabulary
Evaluating Algebraic Expressions
4-8 The Real Numbers
The set of real numbers is all numbers that can be written on a number line. It consists of the set of rational numbers and the set of irrational numbers.
Irrational numbersRational numbers
Real Numbers
Integers
Wholenumbers
Evaluating Algebraic Expressions
4-8 The Real Numbers
Recall that rational numbers can be written as the quotient of two integers (a fraction) or as either terminating or repeating decimals.
3 = 3.84 5
= 0.623
1.44 = 1.2
Evaluating Algebraic Expressions
4-8 The Real Numbers
A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Caution!
Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. For example, 2 is not a perfect square, so 2 is irrational.
Evaluating Algebraic Expressions
4-8 The Real NumbersMake a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals.
Naturals1, 2, 3...
Wholes0
Integers-3 -19
Rationals
2
36
1
4
-2.65
Irrationals2
Reals
Evaluating Algebraic Expressions
4-8 The Real NumbersAdditional Example 1: Classifying Real Numbers
Write all classifications that apply to each number.
5 is a whole number that is not a perfect square.
5
irrational, real
–12.75 is a terminating decimal.–12.75rational, real
16 2
whole, integer, rational, real
= = 24 2
16 2
A.
B.
C.
Evaluating Algebraic Expressions
4-8 The Real NumbersCheck It Out! Example 1
Write all classifications that apply to each number.
9
whole, integer, rational, real
–35.9 is a terminating decimal.–35.9rational, real
81 3
whole, integer, rational, real
= = 39 3
81 3
A.
B.
C.
9 = 3
Evaluating Algebraic Expressions
4-8 The Real Numbers
A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.
Evaluating Algebraic Expressions
4-8 The Real Numbers
State if each number is rational, irrational, or not a real number.
21
irrational
0 3
rational
0 3
= 0
Additional Example 2: Determining the Classification of All Numbers
A.
B.
Evaluating Algebraic Expressions
4-8 The Real Numbers
not a real number
Additional Example 2: Determining the Classification of All Numbers
4 0
C.
State if each number is rational, irrational, or not a real number.
Evaluating Algebraic Expressions
4-8 The Real Numbers
23 is a whole number that is not a perfect square.
23
irrational
9 0
undefined, so not a real number
Check It Out! Example 2
A.
B.
State if each number is rational, irrational, or not a real number.
Evaluating Algebraic Expressions
4-8 The Real Numbers
64 81
rational
8 9
=8 9
64 81
C.
Check It Out! Example 2
State if each number is rational, irrational, or not a real number.
![[Ivan Niven] Irrational Numbers(BookFi.org)](https://static.fdocuments.us/doc/165x107/55328d634a79599f5e8b4631/ivan-niven-irrational-numbersbookfiorg.jpg)
