This document discusses key concepts in decimal notation and operations. It introduces the decimal number system and order of operations. It then covers exponent notation rules, scientific notation, and dimensional analysis. Examples are provided to demonstrate operations, scientific notation, and solving conversion problems using dimensional analysis. The class agenda indicates there will be a review of concepts from the previous week before exploring these topics in more detail.

1. Decimal Notation and Operations Class 2 – Number Systems I

2. Introduction

3. Agenda Warm-up: Brain Teasers Review Follow-up from Week 1 The Decimal System Operations and Order Exponential Values and Operations Scientific Notation Dimensional (Unit) Analysis Assignment 1: Basic Math 1 - Applied Math Quest: Problem-Solving Approaches*

4. A Mathematical Paradox Activity: 3 men and a hotel room

5. The Decimal System Positional Number Systems 123,456

6. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

7. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

8. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

9. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

10. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

11. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

12. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2*17

13. Order of Operations In the following equation, what operations go first? (3a2+ 2ab – 5)3/7 + a2 *17

14. Notation Exponents Xo=1 X1=x X-1=1/x X-3=1/x3 Product Rule a€R:a≠0, am • ak = am+k Quotient Rule a€R:a≠0, ax / ay = a x-y Power Rule (am)n = amn Product to Power Rule (ab)n = anbn

15. Notation Exponents Xo=1 X1=x X-1=1/x X-3=1/x3 Root √x 3√a Calculator Functions Product Rule a€R:a≠0, am • ak = am+k Quotient Rule a€R:a≠0, ax / ay = a x-y Power Rule (am)n = amn Product to Power Rule (ab)n = anbn

16. Notation Scientific Notation Calculator exercise ((12345)6)6 Mantissa always positive >0 and <10 4.765 E+5 or 4.765 x 105 = 476,500 3.20 x 10-3 = .00320 Significant digits 43,210 = 4.321 x 104

17. Dimensional (Unit) Analysis Generally involve conversion of ratios e.g. Miles/Hr Characters/Line Km/Litre Practice Yarmouth Trip110 km/hr Yarmouth = 375 kmHow long in minutes? Archimedes Universe 2.3 x 106m Universe DiameterLight travels at 300,000km/secondHow long for light to cross this universe?

18. Summary Positional Number Systems - Decimal Order of Operations Notation Exponents Scientific Notation Dimensional Analysis Questions?

19. Assignment Assignment 1: Math Basics Due start of next class