rational vs. irrational
DESCRIPTION
Rational Vs. Irrational. Making sense of rational and Irrational numbers. Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko. - PowerPoint PPT PresentationTRANSCRIPT
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Rational Vs. Irrational Rational Vs. Irrational Rational Vs. Irrational Rational Vs. Irrational
Making sense of rational and Irrational numbers
Making sense of rational and Irrational numbers
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AnimalReptile
Biologists classify animals based on shared characteristics. The horned lizard is an animal, a reptile, a lizard, and a gecko.
You already know that some numbers can be classified as whole numbers, integers, or rational numbers. The number 2 is a whole number, an integer, and a rational number. It is also a real number.
LizardGecko
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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
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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
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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.
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Additional Example 1: Classifying Real NumbersWrite 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.
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Check 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
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A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.
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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.
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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.
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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.
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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.
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Lesson Quiz
Write all classifications that apply to each number.
1. 2. –
State if each number is rational, irrational, or not a real number.
3. 4.
2
4 • 9
16 2
25 0
not a real number rational
real, irrational real, integer, rational