Numerical Value

1
Numerical Value

• Scientific Notation and Significant Figures (aka
  sig figs)

2
Numerical Short Cut

• Scientific Notation (sci not)

• Are a set of rules, using the power of ten to
  shorten the number.

3
Moving the Decimal Left

• What happens when you move the decimal left?

• Makes the number SMALLER
• Numbers have positive exponents
• Exponent value number of times you move the
  decimal

4
Practice Scientific Notation

• Write in scientific notation
• 1, 000
• 1.0 x 103
• 258, 000
• 2.58 x 105

5
Practice Sci Not (Individual)

• Write in scientific notation
• 2, 567, 000
• 340
• 56, 000, 000, 000, 000
• 6

6
Moving the Decimal Right

• What happens when you move the decimal right?

• Makes the number BIGGER
• Numbers have negative exponents
• Exponent value number of times you move the
  decimal

7
Practice Scientific Notation

• Write in scientific notation
• 0.015
• 1.5 x 10-2
• 0.0 000 258
• 2.58 x 10-5

8
Practice Sci Not (Individual)

• Write in scientific notation
• 0.000 000 002 567
• 0.340
• 0.000 000 000 000 0560
• 0.00 006

9
Homework Scientific Notation

• Chapter 2, Section 2 (2.2) Page 41
• Problem 11 (complete one a-d)
• Problem 11 (complete one e-h)
• Problem 12 (complete a and b)

10
Significant Figures

• Significant Figures (numbers)

• Are sets of rules that show the best value for a
  number.

11
Nonzero Numbers

• Nonzero numbers are any number whose value is not
  zero.
• Here are some examples of nonzero numbers
• 1
• 22
• 1, 789, 958

12
Nonzero Numbers - Rules

• Count ALL nonzero numbers.
• How many nonzero numbers are in each problem?
• 12
• Two so two sig figs
• 1135
• Four so four sig figs

13
Practice Nonzero (Solo)

• How many significant figures are in the numbers
  below?
• 132, 456
• 7, 896
• 9

14
Practice Nonzero (Solo)

• Answers
• How many significant figures are in the numbers
  below?
• 132, 456 6 sig fig
• 7, 896 4 sig fig
• 9 1 sig fig

15
Zeros Between Numbers

• Zeros between numbers

• Zeros between two nonzero numbers are
  significant.
• Count all zeros between numbers.

16
Practice Zeros b/w Numbers

• How many significant figures are in each
  example?
• 1001 -
• 10.005 -
• 805 -

17
Practice Zeros b/w Numbers

• Answers
• How many significant figures are in each
  example?
• 1001 4 sig fig
• 10.005 5 sig fig
• 805 3 sig fig

18
Whole Number Zeros

• Zeros to right

• All zeros to the right (gt) of a number are NOT
  significant unless there is a DECIMAL point.

19
Practice Zeros to Right

• How many sig figs?

• 10 1 sig fig

20
Practice Zeros to Right

• How many sig figs?

• 15000 2 sig figs

21
Significant Figures

• How many sig figs?

• 150. 3 sig figs

150.
22
Practice Zeros to right

• How many significant figures are in each
  example?
• 100 -
• 10.00 -
• 800, 000 -

23
Zeros with Decimals

• Zeros WITH the decimals

• All zeros to the left (?) of the first nonzero
  number are not significant.

24
Practice Zeros with Decimals

• How many sig figs?

• 0.000 000 15
• 0.00000015
• 2 sig figs

25
Practice Zeros with Decimals

• How many sig figs?

• 0.01
• 0.01
• 1 sig figs

26
Zeros with Decimals

• Zeros WITH the decimals

• Zeros to the right (?) of the last nonzero number
  are significant

27
Practice Zeros with Decimals

• How many sig figs?

• 0.150 000 00
• 0.150 000 00
• 8 sig figs

28
Practice Zeros with Decimals

• How many sig figs?

• 0.0000010
• 0.0000010
• 2 sig figs

29
Practice Zeros (individual)

• How many sig figs?

• 0.015
• 0.1500
• 0.0010100

30
Practice Zeros (individual)

• How many sig figs?
• Answers

• 0.015 2 sig figs
• 0.1500 4 sig figs
• 0.0010100 5 sig figs

31
Video sig figs (a way to practice)

• https//www.youtube.com/watch?vpuvE8hF6zrY

32
Practice All the Rules

• You try it!

1. 360000
2. 5060
3. 360.0100
4. 0.00485
5. 1.00 x 1010

33
Homework Scientific Notation

• Chapter 2, Section 3 (2.3) Page 51
• Problem 35 (a and b)
• Problem 36 (a and b)
• Problem 37

34
Calcuations Add/Subtract

• Calculations Add/Subtract

• Do all the math first.
• The final answers sig figs will depend on the
  number with the least number of decimals.

35
Practice Add/Subtract

• Report Answer in Correct Sig Figs

• 1.02.120.65
• 15.5952.4456-2.9

36
Practice Add/Subtract

• Report Answer in Correct Sig Figs

• 1.02.120.65
• 3.77 (1 decimal place)
• 3.8

37
Practice Add/Subtract

• Report Answer in Correct Sig Figs

• 15.5952.4456-2.9
• 15.1406 (1 dec. place)
• 15.1

38
Practice Add/Subtract (solo)

• Report Answer in Correct Sig Figs

• 161.7
• 12.037-3.93
• 0.073 10.0037
• 3.78 x 104 -2.3 x 103

39
Practice Add/Subtract (solo)

• 161.7 17.7 18
• 12.037-3.93 8.107000000000001 8.11
• 0.073 10.0037 10.0767 10.077
• 3.78 x 104 -2.3 x 103 35500 3.55 x 104

• Report Answer in Correct Sig Figs

40
Calculation Mult/Div

• Calculations Multiplication/Division

• Do all the math first.
• The final answers sig figs will depend on the
  number with the least number of sig figs.

41
Practice Mult/Div (Group)

• Report answer in the correct number of
  significant figures.
• 10x2.75/0.500
• (2.00 x 102)(0.2056)

42
Practice Mult/Div (Group)

• Report answer in the correct number of
  significant figures.
• 10x2.75/0.500 55 60
• (2.00 x 102)(0.2056) 41.12 41.1

43
Practice Mult/Div (Indiv)

• Report answer in the correct number of
  significant figures.
• (5.5)3
• 45 3.00
• 45 3

44
Practice Mult/Div (Indiv)

• Report answer in the correct number of
  significant figures.
• (5.5)3 166.375 170
• 45 3.00 135 140
• 45 3 135 100

45
All Answer in Correct Sig Fig

1. 4
2. 222
3. 8700
4. 30.4020
5. 2005x18.36x2.3
6. 20.4x0.5
7. 2.280.80171
8. 2.40.050.00123456
9. 222-2.006X102/10.0
10. 750x0.342.62/20

46
All Answer in Correct Sig Fig

• You try it! Tell which rule to use and number of
  sig figs. For math, report answer in correct
  sig. figs.

1. 1 sig fig
2. 3 sig fig
3. 2 sig fig
4. 6 sig fig
5. 84667.14 84000 or 8.4x104
6. 10.2 10 or 1 x 101
7. 154.001 154
8. 2.45123456 2.5
9. 22.202006 22.2
10. 745.5882353 700 or 7 x 101

47
Alternatives Considered

• Homework
• problems 212 (a, b, e, f)
• problems 213 (a-d)
• problems 214 (e, f, g, h)
• problems 215 (a-d)
• problems 216 (a-d)
• Or worksheet!

48
Websites for help

• Uncertainty in Measurements - http//antoine.frost
  burg.edu/cgi-bin/senese/tutorials/sigfig/index.cgi
  
• Significant Figures - http//science.widener.edu/s
  vb/tutorial/sigfigurescsn7.html
• Applet Significant Figures - http//www.lon-capa.
  org/mmp/applist/sigfig/sig.htm
• Significant Figures Games - http//www.mangahigh.c
  om/en_us/maths_games/number/rounding_accuracy_and_
  estimation/round_using_significant_figures
• Significant Figures Explanation -
  https//www.youtube.com/watch?vpuvE8hF6zrY
• Adding and Subtractinghttp//sigfigscalculator.ap
  pspot.com/tutorial/add_and_subtract