Rational Numbers: Concepts and Representations
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Questions and Answers

What is a characteristic of an irrational number?

  • It can be expressed as a finite decimal or fraction
  • It has a non-terminating and non-repeating decimal expansion (correct)
  • It is a whole number
  • It can be written in the form a/b, where a and b are integers and b ≠ 0

    • What is the purpose of finding the simplest form of a fraction?

  • To convert the fraction to a decimal
  • To make the fraction more complicated
  • To eliminate any common factors between the numerator and denominator (correct)
  • To find the equivalent ratio of the fraction

    • What is a repeating decimal?

  • A decimal that has a non-terminating and non-repeating sequence of digits
  • A decimal that ends after a finite number of digits
  • A decimal that has a sequence of digits that repeats indefinitely (correct)
  • A decimal that can be expressed as a finite fraction

    • What is the purpose of ratios?

    <p>To compare two quantities and describe their proportions and rates</p> Signup and view all the answers

    What is an equivalent ratio?

    <p>A ratio that has the same value as the original ratio, but a different form</p> Signup and view all the answers

    What is a terminating decimal?

    <p>A decimal that ends after a finite number of digits</p> Signup and view all the answers

    Study Notes

    Rational Numbers

    Irrational Numbers

    • A number that cannot be expressed as a finite decimal or fraction
    • Examples: π, e, √2
    • Cannot be written in the form a/b, where a and b are integers and b ≠ 0
    • Non-terminating and non-repeating decimal expansion

    Fractions

    • A way to represent a rational number as a quotient of two integers
    • Form: a/b, where a is the numerator and b is the denominator
    • Equivalent fractions: fractions that have the same value, but different forms
    • Simplest form: a fraction in which the numerator and denominator have no common factors

    Decimals

    • A way to represent a rational number in base 10
    • Terminating decimal: a decimal that ends after a finite number of digits
    • Repeating decimal: a decimal that has a sequence of digits that repeats indefinitely
    • Converting fractions to decimals: dividing the numerator by the denominator

    Ratios

    • A comparison of two quantities
    • Form: a:b or a/b, where a and b are quantities being compared
    • Equivalent ratios: ratios that have the same value, but different forms
    • Used to describe proportions and rates

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    Description

    Test your understanding of rational numbers, including irrational numbers, fractions, decimals, and ratios. Learn how to represent and manipulate these numbers in different forms.

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