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# Class 2 Math I

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In this class we will examine the decimal number system, operations and notation. We will also examone math operations on positional number systems and begin to explore dimensional (unit) analysis and calculations.

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### Class 2 Math I

1. 1. Decimal Notation and Operations<br />Class 2 – Number Systems I<br />
2. 2. Introduction<br />
3. 3. Agenda<br />Warm-up: Brain Teasers<br />Review Follow-up from Week 1<br />The Decimal System<br />Operations and Order<br />Exponential Values and Operations<br />Scientific Notation<br />Dimensional (Unit) Analysis<br />Assignment 1: Basic Math 1 - Applied Math<br />Quest: Problem-Solving Approaches* <br />
4. 4. A Mathematical Paradox <br />Activity: 3 men and a hotel room<br />
5. 5. The Decimal System<br />Positional Number Systems<br />123,456<br />
6. 6. Order of Operations<br />In the following equation, what operations go first?<br /> (3a2+ 2ab – 5)3/7 + a2 *17<br />
7. 7. Order of Operations<br />In the following equation, what operations go first?<br />(3a2+ 2ab – 5)3/7 + a2 *17<br />
8. 8. Order of Operations<br />In the following equation, what operations go first?<br />(3a2+ 2ab – 5)3/7 + a2 *17<br />
9. 9. Order of Operations<br />In the following equation, what operations go first?<br />(3a2+ 2ab – 5)3/7 + a2 *17<br />
10. 10. Order of Operations<br />In the following equation, what operations go first?<br />(3a2+ 2ab – 5)3/7 + a2 *17<br />
11. 11. Order of Operations<br />In the following equation, what operations go first?<br /> (3a2+ 2ab – 5)3/7 + a2 *17<br />
12. 12. Order of Operations<br />In the following equation, what operations go first?<br /> (3a2+ 2ab – 5)3/7 + a2*17<br />
13. 13. Order of Operations<br />In the following equation, what operations go first?<br /> (3a2+ 2ab – 5)3/7 + a2 *17<br />
14. 14. Notation<br />Exponents<br />Xo=1<br />X1=x<br />X-1=1/x<br />X-3=1/x3<br />Product Rule<br /> a€R:a≠0, am • ak = am+k<br />Quotient Rule<br /> a€R:a≠0, ax / ay = a x-y<br />Power Rule<br /> (am)n = amn<br />Product to Power Rule<br /> (ab)n = anbn<br />
15. 15. Notation<br />Exponents<br />Xo=1<br />X1=x<br />X-1=1/x<br />X-3=1/x3<br />Root<br />√x<br />3√a<br />Calculator Functions <br />Product Rule<br /> a€R:a≠0, am • ak = am+k<br />Quotient Rule<br /> a€R:a≠0, ax / ay = a x-y<br />Power Rule<br /> (am)n = amn<br />Product to Power Rule<br /> (ab)n = anbn<br />
16. 16. Notation<br />Scientific Notation<br />Calculator exercise<br />((12345)6)6<br />Mantissa always positive >0 and <10<br /> 4.765 E+5 or 4.765 x 105 = 476,500<br />3.20 x 10-3 = .00320<br />Significant digits 43,210 = 4.321 x 104<br />
17. 17. Dimensional (Unit) Analysis<br />Generally involve conversion of ratios<br />e.g. Miles/Hr Characters/Line Km/Litre<br />Practice<br />Yarmouth Trip110 km/hr Yarmouth = 375 kmHow long in minutes?<br />Archimedes Universe<br />2.3 x 106m Universe DiameterLight travels at 300,000km/secondHow long for light to cross this universe?<br />
18. 18. Summary<br />Positional Number Systems - Decimal<br />Order of Operations<br />Notation<br />Exponents<br />Scientific Notation<br />Dimensional Analysis<br />Questions?<br />
19. 19. Assignment<br />Assignment 1: Math Basics<br />Due start of next class<br />