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MathReview - Mathematics Review Physics 110 Dr Jeff Lewis...

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Mathematics Review Physics 110 Dr. Jeff Lewis ©2010

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Units All physical quantities have units . Units are the scale of measure being used. A time interval of “5” is meaningless unless you specify the units (months, hours, seconds, or whatever). You will be expected to always include the units in your answers. [Material covered today is in the textbook Appendix (pp 531-533) and Preview section P.9.]
Metric System We will use the metric (or SI) system in this course! Most of you are probably more familiar with U.S. units, so why use the metric system? Because: 1. It is an easier and better system. 2. The metric system is the standard system used in every country in the world except one (the U.S.). 3. If you don’t know it, it’s about time you learn!

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Base Quantities in the Metric System Length: meter (m) Mass: kilogram (kg) Time: second (s) These particular units are not what makes the metric system the better system. The real strength of the metric system is that there is a standard set of prefixes for making larger or smaller units and these all change the units by simple factors of 10 or 100 or 1000 etc.
Metric Prefixes Prefix Abbr. Factor Example: kilo k 1000 (=10 3 ) 1 kg = 1000 g mega M 1,000,000 = 10 6 1 Mg = 1,000,000 g giga G 10 9 = billion Won’t be used much tera T 10 12 = trillion Won’t be used much centi c .01 = 1 / 100 1 cm = .01 m milli m .001 = 1 / 1000 1 ms = .001 s micro μ 10 -6 = 1 / 1000000 1 μs = .000 001 s nano n 10 -9 1 nm = 10 -9 m pico p 10 -12 Won’t be used

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Learn the Metric System! That is, learn the prefixes (the one’s that will be used) and what factor they represent. There will be at least one question on exam 1 testing whether you have learned the metric system.
Scientific Notation In astronomy, we often deal with very large (and very small!) numbers. Scientific Notation (also known as powers-of-ten notation ) is a system for conveniently dealing with very large and small numbers. Let’s start with some basics about exponents. 10 6 = 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 10 12 = a one followed by 12 zeroes 5.2 x 10 4 = 5.2 x 10 x 10 x 10 x 10 = 5.2 x 10,000 = 52,000

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Scientific Notation (2) Any number written a.aa x 10 b is considered to be in standard scientific notation. More examples: 1.23 x 10 1 = 12.3 10 0 = 1 (multiplying by no factors of ten is equivalent to multiplying by 1, neither changes the number). 10 -8 = (1/10) x (1/10) x … = .000 000 01 note that this is the same as 1 x 10 -8 6.2 x 10 -5 = .000 062 multiplying by 10 n just means moving the decimal place left or right n spots (here it was moved left 5 places).
Scientific Notation on Your Calculator Because we so often deal with very large numbers, you need a scientific calculator for this class. Hopefully you brought yours today, get it out now.

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MathReview - Mathematics Review Physics 110 Dr Jeff Lewis...

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