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 OperationsClass 2 – Number Systems I

2. Introduction

3. AgendaWarm-up: Brain TeasersReview Follow-up from Week 1The Decimal SystemOperations and OrderExponential Values and OperationsScientific NotationDimensional (Unit) AnalysisAssignment 1: Basic Math 1 - Applied MathQuest: Problem-Solving Approaches*

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

5. The Decimal SystemPositional Number Systems123,456

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

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

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

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

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

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

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

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

14. NotationExponentsXo=1X1=xX-1=1/xX-3=1/x3Product Rule a€R:a≠0, am • ak = am+kQuotient Rule a€R:a≠0, ax / ay = a x-yPower Rule (am)n = amnProduct to Power Rule (ab)n = anbn

15. NotationExponentsXo=1X1=xX-1=1/xX-3=1/x3Root√x3√aCalculator Functions Product Rule a€R:a≠0, am • ak = am+kQuotient Rule a€R:a≠0, ax / ay = a x-yPower Rule (am)n = amnProduct to Power Rule (ab)n = anbn

16. NotationScientific NotationCalculator exercise((12345)6)6Mantissa always positive >0 and <10 4.765 E+5 or 4.765 x 105 = 476,5003.20 x 10-3 = .00320Significant digits 43,210 = 4.321 x 104

17. Dimensional (Unit) AnalysisGenerally involve conversion of ratiose.g. Miles/Hr Characters/Line Km/LitrePracticeYarmouth Trip110 km/hr Yarmouth = 375 kmHow long in minutes?Archimedes Universe2.3 x 106m Universe DiameterLight travels at 300,000km/secondHow long for light to cross this universe?

18. SummaryPositional Number Systems - DecimalOrder of OperationsNotationExponentsScientific NotationDimensional AnalysisQuestions?

19. AssignmentAssignment 1: Math BasicsDue start of next class