Introduction to Number Systems
ch1-introduction
Rational Numbers
ch1-rational-numbers
Exercise 1.1 - Detailed Solutions
ch1-exercise-1-1
Irrational Numbers
ch1-irrational-numbers
Exercise 1.2 - Detailed Solutions
ch1-exercise-1-2
Real Numbers & Decimal Expansions
ch1-real-decimals
Exercise 1.3 - Detailed Solutions
ch1-exercise-1-3
Operations on Real Numbers
ch1-operations
Rationalizing the Denominator
ch1-rationalization
Exercise 1.4 & 1.5 - Solutions
ch1-exercise-1-4-5
Laws of Exponents for Real Numbers
ch1-laws-exponents
Chapter 1 Summary
ch1-summary
What is a Polynomial?
ch2-introduction
Types of Polynomials
ch2-types
Zeroes of a Polynomial
ch2-zeroes
Exercise 2.1 - Detailed Solutions
ch2-exercise-2-1
Remainder Theorem
ch2-remainder-theorem
Factor Theorem
ch2-factor-theorem
Algebraic Identities
ch2-identities
Exercise 2.4 - Identity Applications
ch2-exercise-2-4
Chapter 2 Summary
ch2-summary
A rational number is any number that can be written as qp where:
- p and q are integers
- q=0
It means we can express the number as a fraction of two integers.
Examples of Rational Numbers:
| Number | p/q Form | Why it works |
|---|---|---|
| 5 | 5/1 | Any integer can be written with denominator 1 |
| -3 | -3/1 | Negative integers work too |
| 0.5 | 1/2 | Terminating decimals are rational |
| 0.333... | 1/3 | Repeating decimals are rational |
| 0 | 0/1 | Zero is rational! |
Key Fact: There are infinitely many rational numbers between any two rational numbers!
Method 1: Average Method
Method 2: Common Denominator Method
Interactive Visualization