Podcast Beta
Questions and Answers
What is the definition of a rational number?
A rational number is a real number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
Give an example of an irrational number.
π, e, √2, or √3
What is the result of the sum of a rational number and an irrational number?
The sum is always irrational.
What is the result of the product of a rational number and an irrational number?
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What is the set of rational numbers denoted by?
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What is the set of irrational numbers denoted by?
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Study Notes
Real Numbers
Rational Numbers
- A rational number is a real number that can be expressed as the ratio of two integers, i.e., p/q, where p and q are integers and q ≠ 0.
- Examples: 3/4, 22/7, 1/2
- Rational numbers can be expressed as finite decimals or recurring decimals.
- Rational numbers are either terminating or repeating.
- The set of rational numbers is denoted by Q.
Irrational Numbers
- An irrational number is a real number that cannot be expressed as the ratio of two integers, i.e., it is not a rational number.
- Examples: π, e, √2, √3
- Irrational numbers have infinite non-repeating decimals.
- Irrational numbers are non-terminating and non-repeating.
- The set of irrational numbers is denoted by Q' (or sometimes by R\Q).
Key Properties
- The sum of two rational numbers is always rational.
- The sum of a rational number and an irrational number is always irrational.
- The product of two rational numbers is always rational.
- The product of a rational number and an irrational number is always irrational.
- The set of real numbers is the union of the set of rational numbers and the set of irrational numbers.
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Description
Test your understanding of real numbers, including rational and irrational numbers, their properties, and examples. Learn about the differences between these two types of numbers and how to identify them.
