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Real Numbers Explained: Properties, Classification, and Use
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  • Grado
  • CE 101
  • Institución
  • University Of San Carlos

Explore the fundamental concepts of real numbers with this comprehensive PDF document. This resource covers the classification and representation of real numbers, ordering and inequalities, absolute values, and algebraic expressions. With clear definitions, illustrative examples, and practical exer...

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Información del documento

  • 26 de julio de 2024
  • 20
  • 2023/2024
  • Notas de lectura
  • Mr. rodriguez
  • Todas las clases

Temas

  • real numbers
  • algebra
  • number classification
  • pre calculus
  • engineering
  • inequalities
  • math basics
  • civil engineering
  • highschool

Escuela, estudio y materia

  • University of San Carlos
  • CE 101
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laluzdelsol

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31/08/2022




Real Numbers




What You Should Learn
• Represent and classify real numbers.

• Order real numbers and use inequalities.

• Find the absolute values of real numbers and
the distance between two real numbers.

• Evaluate algebraic expressions and use the
basic rules and properties of algebra.

2




1

, 31/08/2022




Real Numbers




3




Real Numbers
Real numbers are used in everyday life to describe
quantities such as age, miles per gallon, and population.
Real numbers are represented by symbols such as
–5, 9, 0, , 0.666 . . ., 28.21, , , and .
Here are some important subsets (each member of subset
B is also a member of set A) of the set of real numbers.

{1, 2, 3, 4, . . .} Set of natural numbers

{0, 1, 2, 3, 4, . . .} Set of whole numbers

{. . . , –3, –2, –1, 0, 1, 2, 3, . . .} Set of integers


4




2

, 31/08/2022




Real Numbers
A real number is rational when it can be written as the ratio
p/q of two integers, where q ≠ 0. For instance, the numbers

= 0.3333. . . = 0.3, = 0.125, and

= 1.126126 . . . = 1.126 are rational.


The decimal representation of a rational number either
repeats (as in = 3.145) or terminates (as in = 0.5).

A real number that cannot be written as the ratio of two
integers is called irrational. Irrational numbers have infinite
nonrepeating decimal representations.
5




Real Numbers
For instance, the numbers
= 1.4142135 . . .  1.41
and
 = 3.1415926 . . .  3.14

are irrational. (The symbol  means “is approximately equal
to.”) Figure P.1 shows subsets of real numbers and their
relationships to each other.




Subsets of Real Numbers
Figure P.1 6




3

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