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
Real Numbers = Rational Numbers + Irrational Numbers
Every point on the number line represents a real number!
| Fraction | Decimal | Why it terminates |
|---|---|---|
| 1/2 | 0.5 | Denominator = 2 |
| 3/4 | 0.75 | Denominator = 4 = 2² |
| 7/8 | 0.875 | Denominator = 8 = 2³ |
| 1/5 | 0.2 | Denominator = 5 |
Rule: Fraction terminates if denominator has ONLY 2s and 5s as prime factors!
| Fraction | Decimal | Repeating block |
|---|---|---|
| 1/3 | 0.333... | 3 repeats |
| 1/7 | 0.142857142857... | 142857 repeats |
| 1/11 | 0.090909... | 09 repeats |
| 1/6 | 0.1666... | 6 repeats |
The decimal expansion of a rational number is either terminating or non-terminating recurring.
The decimal expansion of an irrational number is non-terminating non-recurring.
Since 1/7 = 0.142857...
All use the SAME digits 142857, just different starting points!
Interactive Visualization