Podcast
Questions and Answers
All whole numbers are also natural numbers.
All whole numbers are also natural numbers.
False
The number $2$ is a composite number.
The number $2$ is a composite number.
False
All rational numbers can be expressed as either terminating or repeating decimals.
All rational numbers can be expressed as either terminating or repeating decimals.
True
Irrational numbers can be expressed as a fraction of two integers.
Irrational numbers can be expressed as a fraction of two integers.
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The process of breaking down a number into its prime factors is called factorization.
The process of breaking down a number into its prime factors is called factorization.
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Study Notes
Number Systems
- Natural Numbers: Positive whole numbers (1, 2, 3, ...)
- Whole Numbers: Non-negative whole numbers (0, 1, 2, ...) - Includes natural and zero.
- Integers: Positive and negative whole numbers. (..., -3, -2, -1, 0, 1, 2, 3, ...) - Includes whole numbers and negatives.
- Rational Numbers: Numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. - Includes terminating and repeating decimals.
- Irrational Numbers: Numbers that cannot be expressed as a fraction and have non-terminating and non-repeating decimals. - Examples include π (pi) and the square root of 2.
Real Numbers
- Real numbers include all rational and irrational numbers.
Prime and Composite Numbers
- Prime Numbers: Whole numbers greater than 1 that have only two factors: 1 and themselves. Examples: 2, 3, 5, 7.
- Composite Numbers: Whole numbers greater than 1 that have more than two factors.
Decimal Types
- Terminating Decimals: Decimals that end after a finite number of digits. Examples: 0.5, 2.75, 1.2
- Repeating Decimals: Decimals that have a repeating pattern of digits. Examples: 0.333..., 0.121212...
Non-Terminating and Non-Repeating Decimals
- These decimals represent irrational numbers. Examples include π and √2.
Factorization
- Factorization is the process of breaking down a number into smaller numbers that multiply to the original number.
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Description
This quiz covers the fundamentals of number systems including natural, whole, integers, rational, and irrational numbers. Additionally, it explores the concepts of prime and composite numbers along with real numbers. Test your understanding of these essential mathematical concepts.
