Numbers & Algebra
Master the Real Number system and unlock the power of Exponents.
Real Numbers
Distinguish between Rational and Irrational numbers using decimal patterns.
Exponent Laws
Apply the laws of multiplication, division, and powers to simplify expressions.
Real World Connections
Why do we need to distinguish these numbers?
- Builders & Carpenters: Precise fraction measurements.
- Electricians: Calculations using irrational constants.
- Plumbers: Volume and flow rate calculations.
- Tech: Coding requires strict variable types.
The Real Number System - Week 1 Term 1 2026
Classify numbers by analysing their decimal expansions.
1. Types of Decimals
Terminating: The digits STOP.
Examples: 0.5, 2.125, 4.0
Recurring: The digits repeat in a pattern forever.
Examples: 0.666..., 0.121212...
Non-Terminating & Non-Recurring: Messy. No pattern. Never ends.
Examples: 3.14159..., √2
Rational (ℚ)
Can be written as a fraction a/b.
- Integers & Whole Numbers
- Terminating Decimals
- Recurring Decimals
Irrational (ℚ')
Cannot be written as a simple fraction.
- Non-terminating decimals
- Non-recurring decimals
- Surds (e.g., √2) and π
Activity: Sort the Numbers
The Real Number System
Exponent Laws - Week 1 Term 1 2026
Simplifying expressions using the first three index laws.
Anatomy
Growth Visualization
Comparing x vs x2 vs x3.
Multiplication Law
When multiplying terms with the same base, ADD the indices.
Interactive Proof
Division Law
When dividing terms with the same base, SUBTRACT the indices.
Visual Cancellation
We removed 2 m's from top and bottom. 5 - 2 = 3.
Power of a Power Law
When raising a power to another power, MULTIPLY the indices.