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Dejalee M
9/21/2023
Algebra 1
Number types with definitions and drawings
A comprehensive guide to different types of numbers in mathematics, exploring classifications from natural numbers to real numbers and their relationships.
9/21/2023
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This section introduces the fundamental number classifications, starting with natural numbers and progressing through whole numbers and integers.
Definition: Whole numbers include all natural numbers plus zero Example: The sequence 0, 1, 2, 3, 4, 5... shows whole numbers Vocabulary: Integers expand upon whole numbers by including negative numbers Example: The sequence ...-3, -2, -1, 0, 1, 2, 3... demonstrates integers
The section also introduces rational numbers, which can be expressed as fractions of integers.
Highlight: All integers are rational numbers Example: Numbers like 1/2, -2, and 3.27 are rational numbers
This page delves into irrational numbers and their relationship to real numbers.
Definition: Irrational numbers cannot be expressed as simple fractions and have non-repeating decimal expansions Example: √5 = 2.2360679774997... is an irrational number Highlight: Real numbers encompass both rational and irrational numbers Example: Numbers like 8, -190, 0, 3, √47, and π are all real numbers
The final section focuses on decimal number properties and classifications.
Definition: Terminating decimals end after a finite number of digits Example: 0.25 is a terminating decimal Vocabulary: Repeating decimals have an infinitely recurring pattern Highlight: All terminating and repeating decimals are rational numbers Example: 1/3 = 0.333... is a repeating decimal
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A comprehensive guide to different types of numbers in mathematics, exploring classifications from natural numbers to real numbers and their relationships.
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This section introduces the fundamental number classifications, starting with natural numbers and progressing through whole numbers and integers.
Definition: Whole numbers include all natural numbers plus zero Example: The sequence 0, 1, 2, 3, 4, 5... shows whole numbers Vocabulary: Integers expand upon whole numbers by including negative numbers Example: The sequence ...-3, -2, -1, 0, 1, 2, 3... demonstrates integers
The section also introduces rational numbers, which can be expressed as fractions of integers.
Highlight: All integers are rational numbers Example: Numbers like 1/2, -2, and 3.27 are rational numbers
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This page delves into irrational numbers and their relationship to real numbers.
Definition: Irrational numbers cannot be expressed as simple fractions and have non-repeating decimal expansions Example: √5 = 2.2360679774997... is an irrational number Highlight: Real numbers encompass both rational and irrational numbers Example: Numbers like 8, -190, 0, 3, √47, and π are all real numbers
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The final section focuses on decimal number properties and classifications.
Definition: Terminating decimals end after a finite number of digits Example: 0.25 is a terminating decimal Vocabulary: Repeating decimals have an infinitely recurring pattern Highlight: All terminating and repeating decimals are rational numbers Example: 1/3 = 0.333... is a repeating decimal
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The mathematical number system encompasses various categories of numbers, each with distinct properties and relationships. This guide explores the fundamental types from natural numbers to real numbers.
Definition: Natural numbers are positive integers without fractional or decimal components Example: The sequence 1, 2, 3, 4, 5... represents the set of natural numbers Highlight: All natural numbers are also whole numbers and integers
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Students uploaded study notes
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