Number Systems
Number systems classify all numbers into sets such as natural, integer, rational, irrational, and real numbers, providing a structured foundation for algebra and analysis.
What You Need to Know
Key Concept Diagram
Natural numbers (N) are positive counting numbers: 1, 2, 3, ...
Integers (Z) include all whole numbers and their negatives: ..., -2, -1, 0, 1, 2, ...
Rational numbers (Q) can be expressed as p/q where p and q are integers and q is not zero
Irrational numbers cannot be written as fractions; they have non-terminating, non-repeating decimals
Real numbers (R) include all rational and irrational numbers combined
Key Vocabulary
Rational number
Any number that can be expressed as a fraction p/q with integer p and non-zero integer q
Irrational number
A real number that cannot be expressed as a fraction, such as pi or sqrt(2)
Integer
Any whole number including zero and negative whole numbers
Real number
Any number that can be placed on a number line, including all rationals and irrationals
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Which of the following is an irrational number?
Question 2
Which set contains all integers?
Question 3
Is the number 0.333... (repeating) rational or irrational?
Key Concepts Summary
- ●Natural numbers (N) are positive counting numbers: 1, 2, 3, ...
- ●Integers (Z) include all whole numbers and their negatives: ..., -2, -1, 0, 1, 2, ...
- ●Rational numbers (Q) can be expressed as p/q where p and q are integers and q is not zero
- ●Irrational numbers cannot be written as fractions; they have non-terminating, non-repeating decimals
- ●Real numbers (R) include all rational and irrational numbers combined