Scientific Measurements in chemistry

1. Chemistry 1
Lesson #1
Scientific Measurements

2. SUBTOPICS:
 Mass, Volume and Density
Scientific Measurements
 Accuracy and Precision
 Error in Experiment
 Scientific Notation
 Significant Figures

3. OBJECTIVES:
1. explain the difference between mass,
volume, and density of a solid using the
correct and appropriate units;
2. investigate the density of commonly used
solids using laboratory equipment, including
writing a scientific report;
3. explain that accuracy and precision are
important to assess the quality of
experimental results;

4. OBJECTIVES:
4. identify sources of error and propose
improvements to enhance measurement
reliability;
5. apply scientific notation and explain how to
determine the proper number of significant
figures in calculations;

5. What are mass
volume, and
density?

6. MASS
Amount of matter in an object
Metric Unit of Mass = gram
Method of Measurements:
• Electronic Balance
• Triple Beam Balance
• Double pan Balance

7. VOLUME
Amount of space occupied by an
object.
Metric Unit of Mass = Liter or cm3
Method of Measurements:
• Length x Width x Height
• Liquid Displacement

8. DENSITY
Mass per unit volume
Metric Unit of Mass = g/ml or g/cm3
Method of Measurements:
Use the formula: mass
volume

9. I. Accuracy, Precision, & Error
A. Accuracy – how close a measurement
comes to the “true value”.
1. Ex: Throwing Darts
true value = bull's-
eye

10. Precision
B. Precision – how close a series of
measurements are together.
1. Ex: Throwing Darts

11. Explanation
Poor Accuracy
Good Precision
Good Accuracy
Good Precision
Poor Accuracy
Poor Precision

12. Error
D. Error – the difference between the
accepted value and the experimental
value.
1. Formula –
2. Error = ex. value – accepted value
| error |
accepted value

13. Example:
1. In class you determine the melting
point of salt is 755 deg C. The actual
value is 805 deg C. What is your
percent error?
 [|755 - 805| / 805] x 100 =
 6.2% error

14. EXPERIMENTAL ERRORS
This are errors
that cannot
eliminates

17. SCIENTIFIC NOTATION
A QUICK WAY TO WRITE
REALLY, REALLY BIG
OR
REALLY, REALLY SMALL NUMBERS.

18. Scientists
are Lazy!!!
They decided that by
using powers of 10, they
can create short versions
of long numbers.

19. Rules for Scientific Notation
To be in proper scientific
notation the number must be
written with
* a number between 1 and 10
* and multiplied by a power of
ten
23 X 105
is not in proper
scientific notation. Why?

20. Soooo
137,000,000 can be
rewritten as
1.37 X 108

22. Now You Try
Using scientific notation,
rewrite the following numbers.
347,000
3.47 X 105
902,000,000
9.02 X 108
61,400
4

23. Convert these:
1.23 X 10-5
.0000123
6.806 X 10-6
.000006806

24. Try These
4,000
4 X 103
2.48 X 103
2,480
6.123 X 106
6,123,000
306,000,000
3.06 X 108

25. Significant Figures
 Scientist use significant figures to
determine how precise a measurement
is
 Significant digits in a measurement
include all of the known digits plus one
estimated digit

26. For example…
 Look at the ruler below
 Each line is 0.1cm
 You can read that the arrow is on 13.3 cm
 However, using significant figures, you must
estimate the next digit
 That would give you 13.30 cm

27. Let’s try this one
 Look at the ruler below
 What can you read before you estimate?
 12.8 cm
 Now estimate the next digit…
 12.85 cm

28. The same rules apply with all
instruments
 The same rules apply
 Read to the last digit that you know
 Estimate the final digit

29. Let’s try graduated cylinders
 Look at the graduated cylinder below
 What can you read with confidence?
 56 ml
 Now estimate the last digit
 56.0 ml

30. One more graduated cylinder
 Look at the cylinder below…
 What is the measurement?
 53.5 ml

31. Rules for Significant figures
Rule #1
 All non zero digits are ALWAYS
significant
 How many significant digits are in the
following numbers?
• 274
• 25.632
• 8.987
• 3 Significant Figures
• 5 Significant Digits
• 4 Significant Figures

32. Rule #2
 All zeros between significant digits are
ALWAYS significant
 How many significant digits are in the
following numbers?
504
60002
9.077
3 Significant Figures
5 Significant Digits
4 Significant Figures

33. Rule #3
 All FINAL zeros to the right of the
decimal ARE significant
 How many significant digits are in the
following numbers?
32.0
19.000
105.0020
3 Significant Figures
5 Significant Digits
7 Significant Figures

34. Rule #4
 All zeros that act as place holders are
NOT significant
 Another way to say this is: zeros are only
significant if they are between significant
digits OR are the very final thing at the
end of a decimal

35. For example
0.0002
6.02 x 1023
100.000
150000
800
1 Significant Digit
3 Significant Digits
6 Significant Digits
2 Significant Digits
1 Significant Digit
How many significant digits are in the following numbers?

36. Rule #5
 All counting numbers and constants
have an infinite number of significant
digits
 For example:
1 hour = 60 minutes
12 inches = 1 foot
24 hours = 1 day

37. How many significant digits are
in the following numbers?
0.0073
100.020
2500
7.90 x 10-3
670.0
0.00001
18.84
2 Significant Digits
6 Significant Digits
2 Significant Digits
3 Significant Digits
4 Significant Digits
1 Significant Digit
4 Significant Digits

38. Rules Rounding Significant
Digits
Rule #1
 If the digit to the immediate right of the last
significant digit is less that 5, do not round up
the last significant digit.
 For example, let’s say you have the number
43.82 and you want 3 significant digits
 The last number that you want is the 8 –
43.82
 The number to the right of the 8 is a 2
 Therefore, you would not round up & the
number would be 43.8

39. Rounding Rule #2
 If the digit to the immediate right of the last
significant digit is greater that a 5, you round
up the last significant figure
 Let’s say you have the number 234.87 and
you want 4 significant digits
 234.87 – The last number you want is the 8
and the number to the right is a 7
 Therefore, you would round up & get 234.9

40. Rounding Rule #3
 If the number to the immediate right of the
last significant is a 5, and that 5 is followed
by a non zero digit, round up
 78.657 (you want 3 significant digits)
 The number you want is the 6
 The 6 is followed by a 5 and the 5 is followed
by a non zero number
 Therefore, you round up
 78.7

41. Rounding Rule #4
 If the number to the immediate right of the
last significant is a 5, and that 5 is followed
by a zero, you look at the last significant digit
and make it even.
 2.5350 (want 3 significant digits)
 The number to the right of the digit you want
is a 5 followed by a 0
 Therefore you want the final digit to be even
 2.54

42. Say you have this number
 2.5250 (want 3 significant digits)
 The number to the right of the digit you
want is a 5 followed by a 0
 Therefore you want the final digit to be
even and it already is
 2.52

43. Let’s try these examples…
200.99 (want 3 SF)
18.22 (want 2 SF)
135.50 (want 3 SF)
0.00299 (want 1 SF)
98.59 (want 2 SF)
201
18
136
0.003
99

44. Scientific Notation
 Scientific notation is used to express
very large or very small numbers
 I consists of a number between 1 & 10
followed by x 10 to an exponent
 The exponent can be determined by the
number of decimal places you have to
move to get only 1 number in front of the
decimal

45. Large Numbers
 If the number you start with is greater than 1,
the exponent will be positive
 Write the number 39923 in scientific notation
 First move the decimal until 1 number is in
front – 3.9923
 Now at x 10 – 3.9923 x 10
 Now count the number of decimal places that
you moved (4)
 Since the number you started with was
greater than 1, the exponent will be positive
 3.9923 x 10 4

46. Small Numbers
 If the number you start with is less than 1, the
exponent will be negative
 Write the number 0.0052 in scientific notation
 First move the decimal until 1 number is in
front – 5.2
 Now at x 10 – 5.2 x 10
 Now count the number of decimal places that
you moved (3)
 Since the number you started with was less
than 1, the exponent will be negative
 5.2 x 10 -3

47. Scientific Notation Examples
99.343
4000.1
0.000375
0.0234
94577.1
9.9343 x 101
4.0001 x 103
3.75 x 10-4
2.34 x 10-2
9.45771 x 104
Place the following numbers in scientific notation:

48. Going from Scientific Notation
to Ordinary Notation
 You start with the number and move the
decimal the same number of spaces as
the exponent.
 If the exponent is positive, the number
will be greater than 1
 If the exponent is negative, the number
will be less than 1

49. Going to Ordinary Notation
Examples
3 x 106
6.26x 109
5 x 10-4
8.45 x 10-7
2.25 x 103
3000000
6260000000
0.0005
0.000000845
2250
Place the following numbers in ordinary notation:

50. II. Significant Figures
Also known as significant digits, represent
the meaningful digits in a number that
reflect its accuracy or precision.
1. Measurements must be recorded with
significant figures.

51. -All other numbers are significant
-zeros may or may not be significant
-leading zeros are not significant
 0.02 1 (sig fig)
-captive zeros are significant
 0.0203 3 (sig figs)
-trailing zeros following the decimal
point are significant
 0.02030 ? (sig figs)
 200 ? (sig figs)
 200.0 ? (sig figs)
4
1
4
Rules

52. Rounding with Sig Figs
-Express the following #’s to 3 sig figs
 421798.076
= 422,000
 0.00099985
= .00100
 1
= 1.00
 8222
= 8,220
 0.42
= .420

53. Scientific Notation
Scientific Notation + Sig figs
A. All #’s in scientific notation are
counted as significant figures.
B. Ex:
3.0200 x 103
= sig figs
2.77 x 106
= sig figs
5
3

54. Significant figures
Adding and subtracted
A. The answer must not contain any sig
figs beyond the place value common to
all #’s
B. Ex: 4.8
+ 2.015
6.8
(not 6.815)

55. Significant figures
Multiplication and Division
A. The answer must not contain more
sig figs than the least # of sig figs.
B. Ex: 3.1
x 4.01
12
(not 12.431)

56. Class Problems
1. How many significant figures?
-123 meters -30.0 meters
-40,506 kg -6.455 x 103
kg
2. 3.45 + 9.001 and 4.22 - 9.0
3. 3.4 x 5.345 and 10.7 / 12.75
4. 6.33 x 103
+ 5.1 x 104

57. Lesson #1: Scientific Measurements
QUIZ #2
GENERAL CHEMISTRY
1

58. ERROR IN EXPERIMENT
#1-2.
Identify the following error in the following laboratory result. Write high
systematic error if poor accuracy and low systematic error if good
accuracy. Write high random error if poor precision and low random error if
good precision.
precise and accurate

59. ERROR IN EXPERIMENT
#3-4.
Identify the following error in the following laboratory result. Write high
systematic error if poor accuracy and low systematic error if good
accuracy. Write high random error if poor precision and low random error if
good precision.
precise but not accurate

60. Determining the Number of Significant Figures
PROBLEM: For each of the following quantities, write the significant figures
(6) 0.1044 g
(5) 0.0030 L (7) 53,069 mL
(9) 57,600. s
(8) 0.00004715 m
(10) 0.0000007160 cm3

61. SIGNIFICANT FIGURES

62. Chemistry 1
Laboratory Performance

63. THANK YOU