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Real Numbers PPT

Published in: Mathematics
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  • Srajit D

    • Bangalore
    • 4 Years of Experience
    • Qualification: B.Tech/B.E.
    • Teaches: Physics, Mathematics, Chemistry, BITSAT, AIEEE, Py...
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A basic ppt which will tell you the exact definition of real numbers. Hope you will find no problem with the definition of real numbers after going through this ppt.

  • 1
    The Real Number System
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    Real Numbers Real numbers consist of all the rational and irrational numbers. The real number system has many subsets: — Natural Numbers - Whole Numbers — Integers
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    Natural Numbers Natural numbers are the set of counting numbers.
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    Whole Numbers Whole numbers are the set of numbers that include 0 plus the set of natural numbers.
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    Integers Integers are the set of whole numbers and their opposites.
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    Rational Numbers Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b b They can always be expressed by using terminating decimals or repeating decimals.
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    Terminating Decimals Terminating decimals are decimals that contain a finite number of digits. Examples: > 36.8 > 0.125
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    Repeating Decimals Repeating decimals are decimals that contain a infinite number of digits. Examples: 0.333... 1.9 7.689689. FYI... The line above the decimal indicate that number repeats.
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    Irrational Numbers Irrational numbers are any numbers that cannot be expressed a as . b They are expressed as non-terminating, non- repeating decimals; decimals that go on forever without repeating a pattern. Examples of irrational numbers: — 0.34334333433334. - 45.86745893.. - (pi) 2
  • 10
    Other Vocabulary Associated with the Real Number System (ellipsis)—continues without end { } (set)—a collection of objects or numbers. Sets are notated by using braces { Finite—having bounds; limited Infinite—having no boundaries or limits Venn diagram—a diagram consisting of circles or squares to show relationships of a set of data.
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    Venn Diagram of the Real Number System Rational Numbers Irrational Numbers
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    Example Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. 117 a. b. . -12.64039. C 6.36 e. -3 g.
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    To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. Rational Numbers Integers 4 Whole Numbers 9 Natural -3 0 Numbers 117 6.36 Irrational Numbers -12.64039...
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    Solution Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number: — 117 is a natural number, a whole number, an integer, and a rational number. is a rational number. — 0 is a whole number, an integer, and a rational number. — -12.64039... is an irrational number. — -3 is an integer and a rational number. — 6.36 is a rational number. is an irrational number. is a rational number. 4 9
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    FYI... For Your Information When taking the square root of any number that is not a perfect square, the resulting decimal will be non-terminating and non-repeating. Therefore, those numbers are always irrational.

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