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Numerical Methods in Science --How many scientists does it take to change a light bulb? --Scientists dont change light bulbs, thats what engineers are.

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Presentation on theme: "Numerical Methods in Science --How many scientists does it take to change a light bulb? --Scientists dont change light bulbs, thats what engineers are."— Presentation transcript:

1 Numerical Methods in Science --How many scientists does it take to change a light bulb? --Scientists dont change light bulbs, thats what engineers are for.

2 Rounding Choose where (at which digit) you want to round. If the NEXT digit is 5 or more, round up; otherwise round down Rounding does not change the size of the number, just its precision.

3 Examples 27,454,352 Round to the nearest million Round to the nearest 100,000th 7432 Round to the nearest ten.0653 Round to the nearest 1000th

4 Examples 27,454,352 Round to the nearest million Round to the nearest 100,000th 7432 Round to the nearest ten.0653 Round to the nearest 1000th

5 Examples 27,454,352 Check Check 7432 Check.0653 Check

6 Examples 27,454,352 Check Check 7432 Check.0653 Check Round down Round up Round down

7 Examples 27,454,352 =27,000,000 (fill in 0s to keep the same size) = (change the 8 to 9, do not fill in 0s after a decimal!) 7432 =7430 (fill in 0 to keep the same size).0653 =.065 (do not fill in 0s after a decimal!)

8 Round to the nearest: 1)1.22 (tenth) 2) (1000 th ) 3)12,900,000(million) 4).00100(10000 th ) 5)3,045,000,000(million) 6).00003(100 th ) 7)7(10)

9 Significant figures All non-zero digits are significant Zeros –A) Leading, not significant. –B) Trapped (by SF)--significant –C) Trailing, with a decimal--significant

10 Which digits are SF? 1)1.22 2) )12,900,000 4) )3,045,000,000 6) )5.30 x 10 14

11 Which digits are SF? 1)1.22 2) )12,900,000 4) )3,045,000,000 6) )5.30 x 10 14

12 Adding and subtracting =

13 Adding and subtracting = 1.67 Your calculator says 1.672, but you dont know how many thousandths there are in the first number. Round where your knowledge ends

14 Adding and subtracting 1) ) ) ) )

15 Adding and subtracting 1) = ) = ) = ) = ) =

16 Multiplying and dividing Suppose there are 20,000 pairs of Nike Air Pegasus running shoes in the Denver area. Suppose each pair cost $53.47, like mine did. How much did those shoes cost?

17 Multiplying and dividing Suppose there are 20,000 pairs of Nike Air Pegasus running shoes in the Denver area. Suppose each pair cost $53.47, like mine did. How much did those shoes cost? $1 million.

18 Multiplying and dividing Suppose there are 20,000 pairs of Nike Air Pegasus running shoes in the Denver area. Suppose each pair cost $53.47, like mine did. How much did those shoes cost? $1 million. Not $1,069,400

19 Multiplying and dividing Round to match the precision of the least number of SF in your problem. The 20,000 pairs is a round number, 1SF. Dont use more than 1SF in your answer.

20 Multiplying and dividing 1) x.047 2)1390 ÷ 150 3).34 x.038 4)5.30 ÷ )3 x 4

21 Multiplying and dividing 1) x.047= )1390 ÷ 150= 9.3 3).34 x.038=.013 4)5.30 ÷ 23521= )3 x 4= 10

22 A little bit of algebra If Density = mass/volume (It does.) then: D=m/v, m=vD, v=m/D and

23 A little bit of algebra You will have to be able to solve for any variable in a formula. The steps are: 1) Start with your original formula. D=m/v

24 A little bit of algebra You will have to be able to solve for any variable in a formula. The steps are: 2) Multiply both sides by v (the denominator) vD=vm/v

25 A little bit of algebra You will have to be able to solve for any variable in a formula. The steps are: 2) Multiply both sides by v (the denominator) vD=vm/v = m V cancels on the right

26 A little bit of algebra You will have to be able to solve for any variable in a formula. The steps are: 3) Divide both sides by D m = vD D

27 A little bit of algebra You will have to be able to solve for any variable in a formula. The steps are: 3) Divide both sides by D m = vD =v D D cancels on the right

28 A little bit of algebra So: D=m/v m=vD v=m/D

29 In general: Solve by undoing If something is added, subtract If something is subtracted, add If something is multiplied, divide If something is divided, multiply If something is raised to a power, take that root Practice, Practice, Practice!

30 Conversions 1) Start with the measurement given. 2) Multiply it by a fraction called a conversion factor. It has three properties: --The units you start with go on the bottom (You want them to cancel) --The units you want go on the top (You want to end up with them next) --The numbers make the top and the bottom equal (So the fraction is equal to 1, it won't change the value of the measurement) 3) Cancel your units, multiply the numerators, and divide by the denominator 4) Repeat if necessary

31 For example: mm = _______ m

32 For example: mm = _______ m mm Start with the measurement given.

33 For example: mm = _______ m mm x ____________ = Multiply it by a fraction called a conversion factor.

34 For example: mm = _______ m mm x ____________ = mm --The units you start with go on the bottom (You want them to cancel)

35 For example: mm = _______ m mm x ________m___ = mm --The units you want go on the top (You want to end up with them next)

36 For example: mm = _______ m mm x __1 x m___ = 1 mm --The numbers make the top and the bottom equal (So the fraction is equal to 1, it won't change the value of the measurement)

37 For example: mm = _______ m mm x __1 x m___=7.432x10 -2 m 1 mm (or.07432m) 3) Cancel your units, multiply the numerators, and divide by the denominator

38 Convert 1)1.26 cm = _____m 2)5.28 m = ______ m 3) km = _______ mm 4)8.00 mm = _______nm

39 Metric System prefixes Prefix Symbol Meaning gigaG10 9 ( ) megaM10 6 ( ) kilok10 3 (1 000) dekadk10 1 (10) decid10 -1 (0.1) centic10 -2 (0.01) millim10 -3 (0.001) microm10 -6 ( ) nanon10 -9 ( )

40 SI System --the International system --used by scientists worldwide --more consistent than the English system --defines seven standard units --allows combinations for derived units (it is no more precise or accurate than any other system)

41 Measurement Unit Symbol Lengthmeterm Masskilogram kg Timeseconds electric currentampereA temperature kelvinK amount of substancemolemol luminous intensitycandela cd

42 Commonly Used Derived Units Area Volume Velocity Acceleration Density Dynamic viscosity

43 Commonly Used Derived Units Area=length x width (in m 2 ) Volume=area x height (in m 3 ) Velocity=length / time (in m/s) Acceleration=velocity / time (in m/s 2 ) Density=mass / volume (in kg/m 3 ) Dynamic viscosity (Just kidding, its not common)

44 For a chemist Mass: gram, kilogram, milligram Length: centimeter, meter, millimeter, nanometer Volume: milliliter, liter, cubic meter Time: second, minute, hour

45 Making measurements Read the numbers Count the marks Estimate one final digit.

46

47

48 Scientific Notation For any real number, A, there is some a and b, such that: A= a x 10 b a is between 1 and 10 b is a whole number

49 Examples 27,000,

50 Examples = 2.7 x = 8.9 x = 7.43 x = 6.5 x 10 -2

51 Examples 5.8 x x x x 10 -3

52 Examples 5.8 x 10 4 = x = x 10 8 = 21,700, x =.00505

53 Put into scientific notation 1)1.22 2) )12,900,000 4) )3,045,000,000 6) )5

54 Take out of scientific notation 1)1.82 x )4.28 x )1.60 x )1.030 x )7.045 x )9 x )4 x 10 1

55 Graphing A graph shows a picture of what a set of numbers represent. The representation must be honest

56 Pie Graphs Used when the total of all of the numbers is some whole valuethis is for all of my AP Chemistry students AP Chemistry Scores, Denver South High School Extremely well qualified Well Qualified Qualified Possibly qualified No recommendation Extremely well qualified Well Qualified Possibly qualified Qualified No recommendation

57 Bar Graphs Used when the categories dont add up to any definite total

58 Line Graphs Used when both sets of data are numbers


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