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Mathematics LibreTexts

3: The Real Number System

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  • 3.1: Introduction to the Real Number System
    The real number system includes all numbers that can be represented on a number line, encompassing natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Understanding this system helps elementary students build a strong foundation for future mathematical learning and practical problem-solving.
  • 3.2: Whole and Natural Numbers
    Understanding whole and natural numbers is fundamental for building a strong mathematical foundation and applying math in real-world scenarios. Natural numbers are the set of positive integers starting from 1 and are used for counting and ordering (1, 2, 3, ...), while whole numbers include all natural numbers plus zero (0, 1, 2, 3, ...). Both sets are essential for basic arithmetic, but they have distinct properties, such as natural numbers not including zero and whole numbers including it. The
  • 3.3: Integer Numbers
  • 3.4: Rational Numbers
  • 3.5: Irrational Numbers
  • 3.6: Real numbers and the Number Line
  • 3.7: Absolute Value
  • 3.8: Adding and Subtracting Integers
  • 3.9: Multiplying and Dividing Integers
    The result of multiplying real numbers is called the product and the result of dividing is called the quotient. A positive number multiplied by a negative number is negative. A negative number multiplied by a negative number is positive. Multiplication is commutative and division is not. When simplifying, work the operations of multiplication and division in order from left to right.
  • 3.10: Fractions
    A fraction is a real number written as a quotient, or ratio, of two integers a and b , where b≠0 .
  • 3.11: Review of Decimals and Percents
    In this section, we provide a brief review of the decimal system. A real number in decimal form, a decimal consists of a decimal point, digits (0 through 9) to the left of the decimal point representing the whole number part, and digits to the right of the decimal point representing the fractional part. The digits represent powers of 10 as shown in the set {…,1,000,100,10,1,1/10,1/100,1/1,000,…}.
  • 3.12: Exponents and Square Roots
  • 3.13: Order of Operations
  • 3.14: Scientific Notation
  • 3.15: Approximation and Estimation
  • 3.16: Real Numbers - Algebra Essentials
    It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Because of the evolution of number systems, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
  • 3.17: Challenges and Misconceptions
  • 3.18: Summary and Review


This page titled 3: The Real Number System is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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