Course 3 Chapter 1 - Real Numbers Flashcards
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Questions and Answers

What is a rational number?

  • A number that cannot be expressed as a ratio
  • A whole number only
  • Numbers that can be written as the ratio of two integers (correct)
  • A number that always ends in 5

    • What is a repeating decimal?

    Decimal form of a rational number.

    What defines a terminating decimal?

    A decimal where the repeating digit is zero.

    What is a power in mathematics?

    <p>A product of repeated factors using an exponent and a base.</p> Signup and view all the answers

    What is the base in a power?

    <p>The number that is the common factor.</p> Signup and view all the answers

    What is an exponent?

    <p>The number of times the base is used as a factor.</p> Signup and view all the answers

    What is a monomial?

    <p>A number, a variable, or a product of a number and one or more variables.</p> Signup and view all the answers

    What is scientific notation?

    <p>A compact way of writing numbers with very large or very small absolute values.</p> Signup and view all the answers

    What is the square root?

    <p>One of the two equal factors of a number.</p> Signup and view all the answers

    What is a perfect square?

    <p>A rational number whose square root is a whole number.</p> Signup and view all the answers

    What does the radical sign represent?

    <p>The symbol used to indicate a positive square root.</p> Signup and view all the answers

    What is a cube root?

    <p>One of three equal factors of a number.</p> Signup and view all the answers

    What is a perfect cube?

    <p>A rational number whose cube root is a whole number.</p> Signup and view all the answers

    What is an irrational number?

    <p>A number that cannot be expressed as the quotient a/b.</p> Signup and view all the answers

    What defines a real number?

    <p>The set of rational numbers together with the set of irrational numbers.</p> Signup and view all the answers

    Study Notes

    Rational Numbers

    • Rational numbers can be represented as the ratio of two integers; the denominator cannot be zero.
    • Includes all integers, fractions, mixed numbers, and percentages.

    Types of Decimals

    • Repeating decimals: Decimal representation of a rational number that has digits that repeat indefinitely.
    • Terminating decimals: A decimal that ends or has a final digit, specifically where the repeating digit is zero.

    Exponents and Powers

    • A power is formed by multiplying a base by itself a certain number of times, indicated by an exponent.
    • The base in a power denotes the number being multiplied, while the exponent indicates how many times the base is multiplied.

    Monomials

    • A monomial can be a number, a variable, or the product of numbers and variables.

    Scientific Notation

    • A method to express very large or very small numbers compactly, such as 5,500 being written as 5.5 x 10^3.

    Roots

    • Square root: The number that, when multiplied by itself, yields the original number; for example, the square root of 144 is 12.
    • Cube root: The number that, when multiplied by itself three times, gives the original number; for example, the cube root of 64 is 4.

    Perfect Squares and Cubes

    • A perfect square is a rational number with an integer as its square root; for instance, 25 is a perfect square because its square root is 5.
    • A perfect cube contains a whole number as its cube root; an example is 27, with a cube root of 3.

    Additional Concepts

    • Radical sign: A symbol used to represent the positive square root of a number.
    • Irrational numbers: Numbers that cannot be expressed as a fraction of two integers, such as √2 or π.
    • Real numbers: Comprises both rational and irrational numbers, forming the complete set of numbers used in mathematics.

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    Description

    Test your knowledge with these flashcards on real numbers from Course 3 Chapter 1. Learn about rational numbers, repeating decimals, and terminating decimals through quick definitions and examples. Perfect for students looking to reinforce their understanding of fundamental mathematical concepts.

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