Podcast
Play an AI-generated podcast conversation about this lesson
Download our mobile app to listen on the go
Get App
Questions and Answers
What are whole numbers?
What are whole numbers?
- Only positive counting numbers
- A number that cannot be expressed as a fraction
- All counting numbers and zero (correct)
- All positive and negative numbers
What defines integers?
What defines integers?
- Numbers that can be written as a fraction
- All positive numbers only
- All negative numbers only
- All positive and negative numbers with no fractional parts and zero. (correct)
What is a rational number?
What is a rational number?
A number that can be written as a fraction of two integers.
Define irrational numbers.
Define irrational numbers.
Signup and view all the answers
What is the result of -54/9?
What is the result of -54/9?
Signup and view all the answers
What type of number is 3√15?
What type of number is 3√15?
Signup and view all the answers
What type of number is 32.343434343...?
What type of number is 32.343434343...?
Signup and view all the answers
What numbers does √81 fall under?
What numbers does √81 fall under?
Signup and view all the answers
What is -2/7 classified as?
What is -2/7 classified as?
Signup and view all the answers
What classifications apply to 0?
What classifications apply to 0?
Signup and view all the answers
What type of number is 23.9?
What type of number is 23.9?
Signup and view all the answers
What does √-25 represent?
What does √-25 represent?
Signup and view all the answers
Flashcards are hidden until you start studying
Study Notes
Classification of Real Numbers
- Whole Numbers: Include all counting numbers and zero, represented as {0, 1, 2, 3, 4, ...}.
- Integers: Encompass all positive and negative whole numbers along with zero, shown as {... -3, -2, -1, 0, 1, 2, 3, ...}.
- Rational Numbers: Defined as numbers that can be expressed as a fraction of two integers (e.g., a/b, where b ≠0).
- Irrational Numbers: Numbers that cannot be expressed as a fraction of two integers; they are characterized by non-repeating and non-terminating decimals.
Examples of Real Numbers
- -54/9: Falls under both integer and rational categories; simplifies to -6.
- 3√15: Classified as an irrational number; cannot be simplified to a fraction.
- 32.343434343...: Considered rational due to its repeating decimal pattern.
- √81: A whole, integer, rational, and natural number as it equals 9.
- -2/7: Recognized as a rational number, being a fraction of two integers.
- 0: Categorized as a whole number, integer, and rational, as it can be written as 0/1.
- 23.9: A rational number classified as a terminating decimal.
- √-25: Not a real number, falls outside the set of real numbers due to the negative square root.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
