Real Numbers Flashcards

Questions and Answers

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?

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?

A number that can be written as a fraction of two integers.

Define irrational numbers.

A number that cannot be expressed as a fraction of two integers; a non-repeating, non-terminating decimal. Signup and view all the answers

What is the result of -54/9?

Integer, Rational Signup and view all the answers

What type of number is 3√15?

Irrational Signup and view all the answers

What type of number is 32.343434343...?

Rational, repeating decimal Signup and view all the answers

What numbers does √81 fall under?

Whole, Integer, Rational, Natural Signup and view all the answers

What is -2/7 classified as?

Rational, fraction of two integers Signup and view all the answers

What classifications apply to 0?

Whole, Integer, Rational Signup and view all the answers

What type of number is 23.9?

Rational, terminating decimal Signup and view all the answers

What does √-25 represent?

Not real Signup and view all the answers

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.

Description

This quiz covers the definitions of various types of real numbers, including whole numbers, integers, rational numbers, and irrational numbers. Test your understanding of these fundamental mathematical concepts and improve your number classification skills.