Quantitative vs. Qualitative

1
Quantitative vs. Qualitative

• Make a quantitative observation about your
  textbook
• Make a qualitative observation about your textbook

2
Quantitative vs. Qualitative

• Quantitative observation
• Qualitative observation

3
Precision vs. Accuracy

• Archery Activity

4
Precision vs. Accuracy

• Which is more precise for measuring volume, a
  beaker or a graduated cylinder?

5
Precision vs. Accuracy

• Accuracy refers to the closeness of
  measurements to the correct or accepted value of
  the quantity measured.
• Precision refers to the closeness of a set of
  measurements of the same quantitiy made in the
  same way.

6
Precision vs. Accuracy

• Measured values that are accurate are close to
  the accepted value
• Measured values that are precise are close to one
  another but not necessarily close to the accepted
  value

7
Darts within small area High precision
Area covered on bulls-eye High accuracy
8
Darts within small area High precision
Area far from bulls-eye Low accuracy
9
Darts within large area Low precision
Area far from bulls-eye Low accuracy
10
Darts within large area Low precision
Area centered around bulls-eye High accuracy
(on average)
11
Unit conversions

• Copy metric conversion from book

12
Unit Conversions

• Practice problems
• 750 km __________m?
• 283 m __________km
• 112 Mwatt __________Kwatt?
• 112 Mwatt __________Gwatt

13
Scientific Notation Significant Figures
14
Unit Estimation
15
Scientific Notation

• Used to make numbers more usable
• 1,000,000,000 1x109
• 0.00000000011x10-10

16
How do you figure this out?

• You move the decimal until you have only one
  digit in front of the decimal.
• If you move right, then the exponent will be
  NEGATIVE based on the number of places your
  decimal moved.
• If you move left, then the exponent will be
  POSITIVE based on the number of places your
  decimal moved.

17
Practice

• Give the following in scientific notation
• 6,289,030,987
• 0.004500678
• 5.60987
• 568.2365400
• 35.98340002
• 0.23476

18
Give the following inscientific notation

• Practice
• 6,289,030,987
• 0.004500678
• 5.60987
• 568.2365400
• 35.98340002
• 0.23476

• 6.289030987x109
• 4.500678x10-3
• 5.60987
• 5.682365400x102
• 3.59834002x10
• 2.3476x10-1

19
Going the other way

• 1.3487x105
• 4.9800456x104
• 2.345x101
• 5.6789x10-3
• 3.591x10-1
• 2.0080x10-2

• 134,870
• 49,800.456
• 23.45
• 0.0056789
• 0.3591
• 0.020080

20
Try For Yourself

• 7.234x10-5?
• 8.234x103?
• 5.000x10-4?
• 9.99998x10-2?
• 8.555x106?

21
ANSWERS
7.234x10-5 0.000 072 34 8.234x103
8,234 5.000x10-4 0.000 500 0 9.99998x10-2
0.099 999 8 8.555x106 8,555,000
22
Significant Digits - What is it?

• When we take measurements in science, we can only
  be sure of our numbers to a certain point
• The numbers we are sure of are called significant
  digits or significant figures (sig figs)

23
Sig Figs - How do we use them?

• Two types
• Measured
• You actually measure and record your answer to a
  certain digit
• Calculated
• You use already measured numbers to compute an
  answer

24
Measured Sig Figs

• Questions you can answer
• How long is your book?
• Measure it with a meterstick and read the length.
• What is the mass of an orange?
• Put it on a scale and read the mass.
• How much milk is in the carton?
• Pour the milk into a graduated cylinder and read
  the volume.

25
Calculated Sig Figs

• Sometimes, youve collected the data and you need
  to calculate a final answer
• Example - you find the length, width and height
  of your book and you want to find the volume.
• You need to multiply the three numbers together
  to get an answer.

26
Determining what countsSig Fig Rules!

• All non-zero numbers are significant
• Example 1,2,3,,9
• All zeros between non-zero numbers are
  significant
• Example 1080.305
• All zeros before a written decimal are
  significant
• Example 600.

27
More Rules

• All zeros following non-zero numbers, after a
  decimal are significant
• Example 1.00 0.003470030
• These rules are to determine what counts when you
  are looking at a number.

28
Practice

• How many sig figs are in the following numbers?
• 2.341
• 0.0004580
• 560
• 560.
• 560.0003

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Answers

• 2.341 has 4 sig figs
• All the numbers are non-zero digits, so they all
  count!

30
Answers

• 0.0004580 has 4 sig figs
• The three non-zero numbers 458 and the zero
  following this set
• The first four zeros are place holders - they get
  the 4 into ten thousands place

31
Answers

• Another way to think about 0.0004580 having four
  sig figs is to write it in scientific notation
• 0.00045804.580x10-4
• When you write in scientific notation, you only
  write the sig figs before you write the
  x10whatever
• So here you see that you wrote the 4, 5, 8, and
  0. Those are the sig figs!

32
Answers

• 560 has 2 sig figs
• This one is tricky. Notice that there is no
  decimal, so the zero is just a place holder to
  get the 6 into the tens spot.

33
Answers

• 560. Has 3 sig figs.
• This time the zero counts because the decimal
  means it was actually measured.

34
Answers

• 560.0003 has 7 sig figs
• All zeros are between non-zero digits, so they
  are all significant.

35
How do you know when to stop?

• When youre measuring, you know when to stop
  based on your equipment.
• If your equipment reads to the tens, then you can
  guess up to one more place. You can read to the
  ones
• Lets look at it.

36
Multi step calculations

• Keep One Extra Digit in Intermediate Answers
• When doing multi-step calculations, keep at least
  one more significant digit in intermediate
  results than needed in your final answer.
• For instance, if a final answer requires two
  significant digits, then carry at least three
  significant digits in calculations. If you
  round-off all your intermediate answers to only
  two digits, you are discarding the information
  contained in the third digit, and as a result the
  second digit in your final answer might be
  incorrect. (This phenomenon is known as
  "round-off error.")

37
2 Greatest Sins in Sig Figs

• Writing more digits in an answer (intermediate or
  final) than justified by the number of digits in
  the data.
• Rounding-off, say, to two digits in an
  intermediate answer, and then writing three
  digits in the final answer.

38
Reading the right number of digits.

• Ruler/Meterstick
• Graduated Cylinder
• Beaker
• Scale

39
Calculations - The rules!!!

• Addition/Subtraction
• Your answer should have the same number of
  decimal places as the number with the least
  number of decimal places
• Multiplication/Division
• Your answer should have the same number of sig
  figs as the number with the least number of sig
  figs
• Always follow the order of operations!

40
Practice

• 2.786 3.5
• 0.0004 x 3001
• 65 45.32 x 90
• 45.6 - 34.23
• 900.3/30.2450

41
Percent Error

• Percent error determines how accurate an
  experimental value is compared quantitatively
  with the correct or accepted value.
• Percent error calculated by subtracting the
  experimental value from the accepted value,
  dividing the difference by the accepted value,
  and then multiplying by 100

42
Percent Error

• Percent error Valueaccepted Valueexperimental
  x 100
• Valueaccepted
• Percent error can have a positive or negative
  value

43
Percent Error

• A student measures the mass and volume of a
  substance and calculates its density as 1.40
  g/mL. The correct, or accepted value of the
  density is 1.36 g/mL. What is the percent error
  of the students measurement?
• 1.36g/mL 1.40 g/mL x 100 -2.9
• 1.36 g/mL

44
Percent Error

• What is your percent error from the lab when you
  found the density of water?
• 1.00g/mL g/mL x 100 -2.9
• 1.00 g/mL

Your experimental value
45
Percent Error pg. 45

• Two technicians independently measure the density
  of a new substance.
• Technician A Records 2.000, 1.999, 2.001 g/mL
• Technician B Records 2.5, 2.9, and 2.7 g/mL
• The correct value is found to be 2.701 g/mL.
• Which Technician is more precise? Which is more
  accurate?

B
A
46
Go Through Answers on Packet
47
Directly Proportional

• Two quantities are directly proportional if
• Dividing one by the other gives a constant value
• y/x k
• k constant
• You can rearrange above equation by saying y
  kx
• If one increasesthe other increases at the same
  rate (doubling one constant doubles the othr
• 2y/2x k (constant)

48
Directly Proportional
All directly proportional relationships produce
linear graphs that pass through the origin
49
Inverse Proportions

• Two quantities are inversely proportional if
• Their product is constant
• xy k
• k constant
• The greater the speed less time to travel a
  given distance
• Double speed (2x) ½ required time
• Halving the speed (½) 2 times the time

50
Inverse Proportional
51
How Sweet It IsChemistry Lab
52
How Sweet It Is Lab

• Benedicts Solution Water Bath Test
• Results
• Beverages should have tested positive if they had
  a sugar sweetener
• Beverages should test negative if they had an
  artificial sweetener

53
How Sweet It Is Lab

• What beverages tested positive?
• What beverages tested negative?
• Evaluate against labels on Sodas

54
How Sweet It Is Lab

• What did you notice about the densities of the
  solutions?
• Which ones had artificial sweeteners? Densities
  less than one?
• Which ones had natural sugar sweeteners?
  Densities more than one?

55
How Sweet It Is Lab

• Analysis Questions
• 1. Evaluate the results against the labels on
  the soda? Record actual sweeteners on a table in
  your lab write-up.
• How accurate were your results?

56
How Sweet It Is Lab

• Analysis Questions
• 2. Which sample do you think had the
  highest/lowest sugar content? Explain why you
  think this.

57
How Sweet It Is Lab

• Application Questions
• 1. How could you prove that carbonated water
  contains no sweetener?

58
How Sweet It Is Lab

• Application Questions
• How could you determine a regular/diet soda by
  using density and not opening the can?
• Immerse in waterwhich one will sinkwhich one
  will float?