8 Questions
Which property of whole numbers states that the result of adding or multiplying whole numbers is always a whole number?
Closure
What is the primary characteristic that distinguishes irrational numbers from rational numbers?
Non-repeating decimal expansion
Which of the following numbers is an example of a rational number?
3/4
What is the result of adding two whole numbers?
Always a whole number
Which property of integers states that the order of integers does not change the result of addition or multiplication?
Commutativity
What is the result of multiplying two rational numbers?
Always a rational number
Which of the following numbers is an example of an irrational number?
π
What is the result of adding two real numbers?
Always a real number
Study Notes
Number System
Introduction
- The number system is a way to represent numbers using digits 0-9.
- It includes whole numbers, integers, rational numbers, and irrational numbers.
Whole Numbers
- Whole numbers are positive integers, including 0, without fractions or decimals.
- Examples: 0, 1, 2, 3, ...
- Properties:
- Closure: The result of adding or multiplying whole numbers is always a whole number.
- Commutativity: The order of whole numbers does not change the result of addition or multiplication.
- Associativity: The order in which whole numbers are added or multiplied does not change the result.
Integers
- Integers include whole numbers and their negative counterparts.
- Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Properties:
- Closure: The result of adding or multiplying integers is always an integer.
- Commutativity: The order of integers does not change the result of addition or multiplication.
- Associativity: The order in which integers are added or multiplied does not change the result.
Rational Numbers
- Rational numbers can be expressed as the ratio of two integers.
- Examples: 3/4, 22/7, 0.5, ...
- Properties:
- Closure: The result of adding, subtracting, multiplying, or dividing rational numbers is always a rational number.
- Commutativity: The order of rational numbers does not change the result of addition or multiplication.
- Associativity: The order in which rational numbers are added or multiplied does not change the result.
Irrational Numbers
- Irrational numbers cannot be expressed as the ratio of two integers.
- Examples: π, e, √2, ...
- Properties:
- Non-terminating and non-repeating decimal expansion.
- Cannot be expressed as a finite decimal or fraction.
Real Numbers
- Real numbers include rational and irrational numbers.
- Properties:
- Closure: The result of adding, subtracting, multiplying, or dividing real numbers is always a real number.
- Commutativity: The order of real numbers does not change the result of addition or multiplication.
- Associativity: The order in which real numbers are added or multiplied does not change the result.
Key Concepts
- Operations on real numbers: addition, subtraction, multiplication, and division.
- Properties of real numbers: closure, commutativity, and associativity.
- Representation of real numbers on the number line.
Number System
Introduction
- A way to represent numbers using digits 0-9.
- Includes whole numbers, integers, rational numbers, and irrational numbers.
Whole Numbers
- Positive integers, including 0, without fractions or decimals.
- Examples: 0, 1, 2, 3, ...
- Properties:
- Closure: Result of adding or multiplying whole numbers is always a whole number.
- Commutativity: Order of whole numbers does not change the result of addition or multiplication.
- Associativity: Order in which whole numbers are added or multiplied does not change the result.
Integers
- Include whole numbers and their negative counterparts.
- Examples: ..., -3, -2, -1, 0, 1, 2, 3, ...
- Properties:
- Closure: Result of adding or multiplying integers is always an integer.
- Commutativity: Order of integers does not change the result of addition or multiplication.
- Associativity: Order in which integers are added or multiplied does not change the result.
Rational Numbers
- Can be expressed as the ratio of two integers.
- Examples: 3/4, 22/7, 0.5, ...
- Properties:
- Closure: Result of adding, subtracting, multiplying, or dividing rational numbers is always a rational number.
- Commutativity: Order of rational numbers does not change the result of addition or multiplication.
- Associativity: Order in which rational numbers are added or multiplied does not change the result.
Irrational Numbers
- Cannot be expressed as the ratio of two integers.
- Examples: π, e, √2, ...
- Properties:
- Non-terminating and non-repeating decimal expansion.
- Cannot be expressed as a finite decimal or fraction.
Real Numbers
- Include rational and irrational numbers.
- Properties:
- Closure: Result of adding, subtracting, multiplying, or dividing real numbers is always a real number.
- Commutativity: Order of real numbers does not change the result of addition or multiplication.
- Associativity: Order in which real numbers are added or multiplied does not change the result.
Key Concepts
- Operations on real numbers: addition, subtraction, multiplication, and division.
- Properties of real numbers: closure, commutativity, and associativity.
- Representation of real numbers on the number line.
Learn about the basics of number systems, including whole numbers, their properties, and examples. Test your understanding of this fundamental math concept.
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