Transcript Measurement - Warren County Schools

Measurement
Scientific Notation
• Rules for Working with Significant Figures:
1. Leading zeros are never significant.
2. Imbedded zeros are always significant.
3. Trailing zeros are significant only if the
decimal point is specified. Hint: Change the
number to scientific notation. It is easier to see.
Scientific Notation
• Addition or Subtraction:
The last digit retained is set by the first
doubtful digit.
• Multiplication or Division:
The answer contains no more significant
figures than the least accurately known
number.
Examples
Example
Number of
Significant
Figures
Scientific
Notation
0.00682
3
6.82 x 10-3
Leading zeros
are not
significant.
1.072
4
1.072 (x 100)
Imbedded
zeros are
always
significant.
300
1
3 x 102
Trailing zeros
are significant
only if the
decimal point
is specified.
300.
3
3.00 x 102
300.0
4
3.000 x 102
Examples
Addition
Even though your
calculator gives you the
answer 8.0372, you must
round off to 8.04. Your
answer must only contain 1
doubtful number. Note
that the doubtful digits are
underlined.
Subtraction
Subtraction is interesting
when concerned with
significant figures. Even
though both numbers
involved in the subtraction
have 5 significant figures,
the answer only has 3
significant figures when
rounded correctly.
Remember, the answer
must only have 1 doubtful
digit.
Examples
Multiplication
The answer must
be rounded off to
2 significant
figures, since 1.6
only has 2
significant figures.
Division
The answer must
be rounded off to
3 significant
figures, since 45.2
has only 3
significant figures.
Rounding
• When rounding off numbers to a certain number of significant figures, do so to the
nearest value.
– example: Round to 3 significant figures: 2.3467 x 104 (Answer: 2.35 x 104)
– example: Round to 2 significant figures: 1.612 x 103 (Answer: 1.6 x 103)
• What happens if there is a 5? There is an arbitrary rule:
– If the number before the 5 is odd, round up.
– If the number before the 5 is even, let it be.
The justification for this is that in the course of a series of many calculations, any
rounding errors will be averaged out.
– example: Round to 2 significant figures: 2.35 x 102 (Answer: 2.4 x 102)
– example: Round to 2 significant figures: 2.45 x 102 (Answer: 2.4 x 102)
– Of course, if we round to 2 significant figures: 2.451 x 102, the answer is definitely 2.5 x
102 since 2.451 x 102 is closer to 2.5 x 102 than 2.4 x 102.
Measurement
• A rule of thumb: read the volume to 1/10 or 0.1 of the
smallest division. (This rule applies to any measurement.)
This means that the error in reading (called the reading
error) is 1/10 or 0.1 of the smallest division on the
glassware.
• The volume in this beaker is 47 1 mL.
You might have read 46 mL;
your friend might read the
volume as 48 mL.
All the answers are correct within
the reading error of 1 mL.
Accuracy v. Precision
Accuracy refers to how closely a measured value agrees with the correct value.
Precision refers to how closely individual measurements agree with each other.
accurate
(the
average is
accurate)
not precise
precise
not
accurate
accurate
and
precise
Metric System
LENGTH
Unit
Abbreviation
Number of
Meters
Approximate U.S.
Equivalent
kilometer
km
1,000
0.62 mile
hectometer
hm
100
328.08 feet
dekameter
dam
10
32.81 feet
meter
m
1
39.37 inches
decimeter
dm
0.1
3.94 inches
centimeter
cm
0.01
0.39 inch
millimeter
mm
0.001
0.039 inch
micrometer
µm
0.000001
0.000039 inch
Metric System
VOLUME
Unit
Abbreviation
Number of
Cubic Meters
Approximate U.S.
Equivalent
cubic meter
m3
1
1.307 cubic yards
cubic decimeter
dm3
0.001
61.023 cubic inches
cubic centimeter
cu cm or
cm3 also cc
0.000001
0.061 cubic inch
Metric System
CAPACITY
Unit
Abbreviation
Number of
Liters
Approximate U.S. Equivalent
cubic
dry
liquid
kiloliter
kl
1,000
1.31 cubic yards
hectoliter
hl
100
3.53 cubic feet
2.84 bushels
dekaliter
dal
10
0.35 cubic foot
1.14 pecks
2.64 gallons
liter
l
1
61.02 cubic
inches
0.908 quart
1.057 quarts
cubic decimeter
dm3
1
61.02 cubic
inches
0.908 quart
1.057 quarts
deciliter
dl
0.10
6.1 cubic inches
0.18 pint
0.21 pint
centiliter
cl
0.01
0.61 cubic inch
0.338 fluid
ounce
milliliter
ml
0.001
0.061 cubic inch
0.27 fluid dram
microliter
µl
0.000001
0.000061 cubic
inch
0.00027 fluid
dram
Metric System
MASS AND WEIGHT
Unit
Abbreviation
Number of
Grams
Approximate U.S.
Equivalent
metric ton
t
1,000,000
1.102 short tons
kilogram
kg
1,000
2.2046 pounds
hectogram
hg
100
3.527 ounces
dekagram
dag
10
0.353 ounce
gram
g
1
0.035 ounce
decigram
dg
0.10
1.543 grains
centigram
cg
0.01
0.154 grain
milligram
mg
0.001
0.015 grain
microgram
µg
0.000001
0.000015 grain
Dimensional Analysis
• Dimensional Analysis is a problem-solving
method that uses the fact that any number or
expression can be multiplied by one without
changing its value.
Dimensional Analysis
• How many centimeters are in 6.00 inches?
• Express 24.0 cm in inches.
Dimensional Analysis
• How many seconds are in 2.0 years?
Mass v. Weight
• 1) Mass is a measurement of the amount of matter
something contains, while Weight is the measurement
of the pull of gravity on an object.
• 2) Mass is measured by using a balance comparing a
known amount of matter to an unknown amount of
matter. Weight is measured on a scale.
• 3) The Mass of an object doesn't change when an
object's location changes. Weight, on the other hand
does change with location.
Volume
•
•
•
•
•
The amount of space occupied by an object
1 L = 1000 mL = 1000 cm 3
1 L = 1 cm 3
1 L = 1.0.57 qt
946.1 ml = 1 qt
Temperature
• Measure of
intensity of
thermal
energy
• What does
this mean?
How hot a
system is…
Conversion Formulas
Density
• Physical characteristic
• Used to id a substance
• d =m/v