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Units of Measurement
SI units (Systeme Internationale d’Unites) were developed so
that scientists could duplicate and communicate their work.
A unit that is defined by a
combination of a base units.
Base Units
Length
meter (m)
Mass
kilogram (kg)
Time
second (s)
Temperature kelvin (K)
Derived Units
Volume
meter cubed (m3)
Density
grams per cubic
centimeter
(g/cm3)
Density
Ratio of an object’s mass to its volume
What happens to density when mass is constant and volume changes?
 Density 
mass
Volume 
 Density 
mass
Volume 
Mass
Density
Mass, Volume and Density Relationships
Volume
DIRECT
Volume
INDIRECT
Temperature Scales
K  C  273
Reliability of Measurements
Accuracy
How close a
measured value is to
an accepted value
vs.
High
Accuracy
Low Accuracy
Low
High
Accuracy
High
Precision
HighAccuracy
Precision
Precision
How close a series of
measurements are to
one another
Percent Error
 Used to evaluate the accuracy of
experimental data.
Error  AcceptedValue  ExperimentalValue
Error
PercentError 
x100
AcceptedValue
Pre-Class Activity
602000000000000000000
000
What is the significance of this number?
How would you express this number in
scientific notation?
Scientific Notation
Coefficient
6.02 x
1023
Exponent
The coefficient must be greater than or equal to one and less than 10.
When expressing numbers less than one (ex. 0.001) in scientific notation, the
decimal point is moved to the right until the coefficient is within range. The
number of spaces moved is used to determine the exponent.
For numbers less than one, the exponent is negative
When expressing numbers greater than 10 (ex. 1000) in scientific notation,
the decimal point is moved to the left until the coefficient is within range. The
number of spaces moved is used to determine the exponent.
For numbers greater than 1, the exponent is positive.
Scientific Notation Calculations
Multiplication and Division
 For multiplication, multiply the coefficients and add the exponents
(1.3 x 104) x (2.0 x 106) = 2.6 x 1010
 Remember, your final answer must be in the correct form. Often,
multiplication of coefficients will yield a number greater than 10. In this case
the result must be changed into the proper form.
(5.3 x 104) x (2.0 x 106) = 10.6 x 1010 = 1.06 x 1011
 For division, divide the coefficients and subtract the exponents. Often,
division of coefficients will result in a value that is less than one. If this
occurs, the final result must be changed into the proper form.
(2.0 x 10-3)  (4.00 x 104) =
0.5 x 10-7 =
5 x 10-8
Scientific Notation Calculations
Addition and Subtraction
 In order to add or subtract numbers in scientific notation, the
exponents of each number has to be the same
 As a rule of thumb, it is best to take the number with the lower
exponent and change it match the higher exponent.
 To increase an exponent, move the decimal point in the coefficient
to left, the number of spaces equal to the increase in the exponent.
 Once the exponents are equal, the coefficients can be added or
subtracted
2.1 x 104
+
1 x 103
+
2.1 x 104
0.1 x 104
2.2 x 104
-
5.37 x 10-4
6.2 x 10-5
-
5.37 x 10-4
0.62 x 10-4
4.75 x 10-4
Pre-class Activity
How long is this paperclip? To what degree
of certainty can it be measured?
Significant Figures in Measurement
Scientists determine the precision of instruments
by the number of digits they report.
Significant Figures in Measurement
Measurements always include all certain
digits and one uncertain digit.
52.7 mL
Measurement Challenge
What value would you
assign to each of these
measurements?
_________ mL
_________ cm
Identifying Significant Figures in Numbers
When examining a number, you determine the number
of digits that are significant by the following rules:
1.All non-zero numbers are significant
2.All final zeros to the right of a decimal are significant
3.Zeros between significant digits are significant
4.
4.For positive numbers less than one, all zeros directly
after the decimal before the first significant figure are
not significant.
5.All zeros at the end of a whole number are not
5.
significant.
6.All contants and counting numbers have an unlimited
number of significant figures.
Sig Fig Challenge
How many sig figs are there in the following
numbers:
1.
2.
3.
4.
5.
0.0004
687
1.0082
330
70.2080
Sig Fig Rules for Calculations
Multiplication and Division
Your answer can not contain more or less sig figs than the
operator that contains the least number of sig figs.
3.86 x 0.45=1.737
1.7
1.737
Identify the significant figures, look on place beyond. If that
digit is 5 or above, round up. If it is less than 5 drop off.
Sig Fig Rules for Calculations
Addition and Subtraction
Your answer can not be more precise than the least
precise operator. Most of the time this means that your
answer must have the same number of decimal places
as the least precise operator
12.38 cm
+2.5 cm
14.88 cm
14.9 cm
1060
cm
+ 23.5 cm
1083.5 cm
1080 cm
If one of the numbers is a whole number that ends in zero(s), then the
final answer must be rounded to the lowest place that contains a nonzero
number.
Metric Conversions
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
o Every metric unit is different from its neighbor
by a factor of ten
o When converting between two units the decimal
point is moved the number of places equal to the
distance between the two unit in the chart
above and in the same direction of movement
Sample problem
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
Convert the following
53 hg = ________dg
Start with 53.
Move the decimal 3 spaces to the right
Fill in the empty spaces with zeros
53
53000 dg
Sample Problem
Move the decimal to the left
K  h  da  b  d  c  m
Move the decimal to the right
Convert the following
300 cg = ________kg
Start with 300.
Move the decimal 5 spaces to the left
Fill in the empty spaces with zeros
300
0.00300 kg
More Practice Problems
K  h  da  b  d  c  m
Convert the following
5.8
0.058 dam = _______
dm
0.0025 L
0.25 cL = _______
109 hg = 10900000
________ mg
Factor Label Method of Conversion
100 cm = 1 m
1 m = 100 cm
100cm
1m
1
1
1m
100cm
Use conversion factors to systematically move from one
unit to the next, cancelling out units on the diagonal in
each step.
Convert
18 m = _______ cm
18m
100 cm
1m
= 1800 cm
Multistep Factor Label Problems
Convert
350 tsp = ______ L
Using the following conversion factors
1 tsp = 5 mL
1 L = 1000 mL
350 tsp
5 mL
1 tsp
1L
1000 mL
= 1.75 L
Multistep Factor Label Practice
Convert 3 min= ______ms
Use 1 min=60 s and 1000 ms = 1 s
Convert 32oz = _____ g
Use 16 oz=1 lb, 2.2 lb = 1kg, 1kg=1000 g
Multidimensional Factor Label Problems
Convert 25 g/mL = ______ kg/dL
• Convert one unit at a time
• Recognize that one unit is in the denominator
25 g
1 mL
1 Kg
1000 g
100mL
1 dL
=2.5kg/dL
Multidimensional Factor Label Practice
Convert 85 km/hr = _________m/s
Convert 0.6 L/min = ________ qt/hr
Use 1qt = 1.1L
Factor Label Practice for Area and Volume
Remember to square or cube the unit as
well as the number when converting to a
squared or cubed unit
1 ft = 12in
Representing Data
Graphing
Circle Graphs (based on percents)
Bar Graphs
(How quantities vary)
Graphing continued
Line Graphs
Dependent Variable
Dependent Variable
In science, we draw a best fit line between data points.
Do not connect the dots.
Independent Variable
Independent Variable
Which graph shows and indirect relationship
between the dependent and independent variable?
Calculating the Slope of a Best Fit Line
Select two points on the line that you have drawn. Do not
select two of your data points because they might not fall
on the line.