Chemistry Mathematics
Measurement
3221.MATH.1; 3221.MATH.2
Learning Goals
• Write the names and abbreviations for the units
used in measurements of length, volume, and
mass
• Label measurements as accurate or precise
• Write a number in scientific notation
• Determine the number of significant figures in
measured numbers
• Adjust calculated answers to the correct number of
significant figures.
• Use numerical prefixes to do metric conversions
through decimal placement.
Units of Measurement
• 2 parts to any measurement: number and unit
• Units are extremely important in reporting
and working with scientific numbers and they
must be included
• The number of digits in a measurement
reflects a degree of precision: the more digits
in the measurement, the more precise it is;
fewer digits, less precision
Why is this important??
Read the following:
• When my son was 7 he walked 3, and when he
was 4 he threw his baseball 8 and said his school
was 5 away.
• When my son was 7 months old he walked 3
steps, and when he was 4 years old he threw his
ball 8 feet and said his school was 5 minutes
away.
• The units make all the difference!!!
Uncertainty in Measurement
• Accuracy: how close a measurement is to the
accepted value
• Precision: degree of “agreement” between
several measurements of the same quantity
• A MEASUREMENT CAN ONLY BE AS PRECISE
AS THE INSTRUMENT USED!!!
Accuracy and Precision Illustration
Two major systems:
1. English system
-used only in the United States
-inches, yards, pounds
2. Metric system
-International System (SI system) is the system of
measurement for the scientific world
-centimeters, meters, kilograms
Fundamental SI Units
Quantity
Symbol
Unit name
Unit abbreviation
Length
l
Meter
m
Mass
m
Kilogram
kg
Time
t
Second
s
Temperature
T
Kelvin
K
Amount of substance
n
Mole
mol
Electric current
I
Ampere
A
Luminous intensity
Iv
Candela
cd
What do the units mean?
• Unit: predefined standard of measurement or
basis of comparison
• Second: 60 s = 1 min
• 1 meter is slightly longer than 1 yard a 100
yd football field is only 91.4 m
• 1 kg = 2.205 lb
Remember: mass is different than weight, which
is affected by gravity
Prefixes in SI system
Prefix
Symbol
Meaning
Exponential Notation
mega-
M
1,000,000
106
kilo-
k
1,000
103
hecto-
h
100
102
deka-
da
10
101
------
-----
1
100
deci-
d
0.1
10-1
centi-
c
0.01
10-2
milli-
m
0.001
10-3
micro-
µ
0.000001
10-6
nano-
n
0.000000001
10-9
Prefix Multipliers
• Used with the standard units of the SI system,
rather than having different “units” with which to
make comparisons
• Multipliers change the value of the unit by powers
of 10
• Prefix multipliers allow us to express a wide range
of measurements in units that are similar in size
to the quantity we are measuring
– Choose the prefix that is most convenient for a
particular measurement
Derived SI Units
Quantity
Symbol
Unit name
Abbreviation
Derivation
Area
A
Square meter
m2
Length x width
Volume
V
Cubic meter
m3
Length x width x height
Density
D
kg/ m3
Mass/volume
Molar mass
M
kg/ mol
Mass/amt of substance
Molar volume
Vm
m3/ mol
Volume/ amt of substance
Energy
E
J
Force x length
Joule
ANY UNIT OF LENGTH, WHEN CUBED (RAISED TO THE
THIRD POWER), BECOMES A UNIT OF VOLUME
1 cm3 = 1 mL 1 dm3 = 1 L
Uncertainty in Measurements
• Measured numbers: numbers you obtain when
you use a measuring tool to determine your
height, weight, or temperature
• To report a measurement, first read the numerical
value of the marked line. Finally, estimate
between the smallest marked lines.
• When an estimate ends on a marked line, a zero is
written for the estimated digit.
Significant Figures
Scientific numbers are recorded so that every digit
is certain except for last, which is estimated.
48.872
When recording measurements, only estimate ONE
digit beyond the smallest division on the
instrument being used!!
Reading Volume
• Meniscus: the curved portion at
the top of a volume of liquid
• Most liquids have a concave
meniscus, however mercury has
a convex meniscus
Rules for determining significant figures:
1. All nonzero digits are significant
1.05
0.0110
2. Interior zeros (zeros between 2 numbers) are
significant
1.0208
50.1
3. Trailing zeros (zeros after a decimal point) are
significant
5.10
3.00
4. Leading zeros ( zeros to the left of the first nonzero
number) are not significant. They only serve to locate
the decimal point.
0.00005
Practice Problems
1.
2.
3.
4.
5.
6.
7.
0.00789
2.0012
0.001
4.100
0.1000
2.65001
100.25
Solutions to Problems
1.
2.
3.
4.
5.
6.
7.
0.00789
2.0012
0.001
4.100
0.1000
2.65001
100.25
3 significant figures (0.00789)
5
(2.0012)
1
(0.001)
4
(4.100)
4
(0.1000)
6
(2.65001)
5
(100.25)
Exact numbers
Exact numbers have an unlimited number of
significant figures
• 3 sources
1. accurate counting of discrete objects
3 atoms means 3.000000 atoms
2. defined quantities
100 cm = 1 m means 100.000 cm =1.00m
3. integral numbers that are part of an
equation
radius = diameter/ 2
Significant Figures in Calculations
• In multiplication or division, the result carries
the same number of significant figures as the
factor with the fewest significant figures
• In addition or subtraction, the result carries
the same number of decimal places as the
quantity carrying the fewest decimal places
Scientific Notation
• Used to write cumbersome numbers in a compact
manner
1.2 x 10-10 exponent (n)
Decimal part
exponential part
To convert a number to scientific notation:
1. move the decimal point to obtain a number between 1 and
10.
2. multiply by 10 raised to the number of places you moved the
decimal point
-if decimal moved left: positive exponent
-if decimal moved right: negative exponent
Practice
Percent Error
• The percentage by which a measurement deviates from the
accepted value
• NO MEASURED VALUE WILL EVER BE EXACT!!
• % Error = Accepted Answer - Experimental Answer x 100
Accepted Answer
Practice Problems
1. Samantha S. Sloppiness measured the volume of her soda before she drank
it for her midmorning snack. She measured the volume of the 12 oz. bottle
to be 14 oz.
2. Clyde Clumsy was directed to weigh a 500 g mass on the balance. After
diligently goofing off for ten minutes, he quickly weighed the object and
reported 458 g.
3. Pretty Patty Pestilence had casually recorded her grades for the nine weeks
in her notebook. She concluded she had 250 points out of 300 for the
grading period. However, Miraculous (chemistry teacher) determined she
had 225 points out of 300 and awarded her a "C" for the grading period.
4. Drew D. Ditzy came to Miraculous with a problem. Drew was told to
measure 50 cm of copper wire to use in an experiment. Since his ruler only
measured to 45 cm he used this amount of wire and his experiment was a
failure.
5. Henry Heavyfoot was just arrested for speeding by Officer O'Rourke for
traveling 65 mph in a 55 mph zone. Henry claimed his speedometer said 55
mph not 65 mph.