Measurement
• Used in everyday life: cooking, taking your
temperature
• Also used extensively in chemistry: mass,
volume, etc.
• Gives you a way to make quantitative
observations about the world around you
Observations
• Qualitative = What is it?
• Quantitative = How much?
• Quantitative observations (measurements)
always include a Number plus a Unit
- 4 inches
- 1 pound
Units of Measurement
• US system, metric and SI
• Metric is most common in science and
medicine
• Know US and Metric units for:
- Length (feet, meters)
- Volume (quarts, liters)
- Mass (pounds, grams)
-Temperature (Fahrenheit, Celsius)
Measuring Length
• When making measurements, estimate one
digit farther than the finest markings
Measuring Volume
• When measuring
volume, always
read at the bottom
of the meniscus
• Remember to
estimate one digit
farther than the
finest markings
Measuring Mass
• When measuring mass, record all of the
digits provided by the scale
Measuring Temperature
• Again, remember to estimate one digit more
than the finest markings on the thermometer
Metric Prefixes
• Use a prefix to relate a unit to its base unit
• Base unit for length is the meter, and kilo = 1000, so
1 kilometer = 1000 meters
• Know metric prefixes and abbreviations for metric
units ( 1 kilometer = 1 km)
• Use the correct abbreviations for units so that you
don’t mix them up
Scientific Notation
• Scientific notation is used to write large or
small numbers
• 1000 = 1 x 103
• 0.001 = 1 x 10-3
• Scientific notation has a coefficient times a
power of 10, where the coefficient is a
number from 1 to less than 10
• Learn to use scientific notation on your
calculator
Measured and Exact Numbers
• When measuring, the last digit is estimated by
reading between the smallest divisions
• Therefore, measured numbers have uncertainty
• Exact numbers have no uncertainty
• Exact numbers come from counting whole
objects, or from definitions:
- There are 33 people in this room
- 100 cm = 1 m
Accuracy vs. Precision
• Accuracy = How close to the true value?
• Precision = How repeatable is the measured value?
x
x x x
xx x
x
x
x
x
x
Precise but not accurate
x
xx
xxxxx
x
Accurate but not precise
Accurate and precise
Significant Figures
• All reported digits in measured numbers are
significant (including the estimated one)
• Sig. Figs. are a measure of uncertainty
• More sig. figs. = less uncertainty
• For numbers ending in zero, it’s best to use
scientific notation to indicate sig. figs.:
500 = 5 x 102 vs. 500. = 5.00 x 102
Sig. Figs. in Measurements
Sig. Figs. In Calculations
• For adding and subtracting: line up decimal places and
use fewest decimal places in answer
5.28 + 3.1 + 4.002 = 12.382 on calculator
Correct sig. figs. = 12.4
• For multiplying and dividing: use least sig. figs. in answer
2.3 x 1.11 = 2.553 on calculator
Correct sig. figs. = 2.6
• Always carry all decimal places through multi-step
calculations and then adjust sig. figs. at end
Unit Conversions
• To convert from one unit to another, a
conversion factor is used
• The conversion factor comes from an equality
• Example: 1 kg = 1000 g can become
1 kg/1000 g
or
1000 g/1 kg
Solving Unit Conversion Problems
1. State given information
2. State unit plan
3. State equality and conversion factors
4. Set up calculation
5. Cancel units and calculate answer
6. Correct sig. figs.
Example Unit Conversion Problem
•
A marathon is 26.2 miles long. How long is
it in kilometers?
1. Marathon = 26.2 miles
2. mi  km
3. 1 km = 0.621 mi
so, 1 km/0.621 mi
4. 26.2 mi x 1 km/0.621 mi =
km
5. 26.2 mi x 1 km/0.621 mi = 42.19001 km
6. Correct sig. figs. = 42.2 km
Temperature Conversions
• Three temperature scales are Fahrenheit, Celsius
and Kelvin
• F = 1.8C + 32
• C = F - 32(0.555)
• K = C + 273.15
• For example:
Dry ice at -56.5C is at -69.7F and is at 216.7 K
Percent Calculations
• % = (part/whole) x 100%
• Percent can be used as a conversion factor
20% can be 20/100 or 100/20
• Example:
If wine is 13% alcohol (by volume), how
many mL of alcohol are in 125 mL of wine?
(125 mL wine) x (13 mL alcohol/100 mL wine)
= 16 mL alcohol
Density
• Density is a measure of how much mass there
is per volume:
d = m/V
• Helium is less dense than air, so a helium
balloon floats
• Copper and zinc are more dense than water, so
a penny sinks in the wishing well
• Density can be in any units of mass/volume
(g/mL, g/L, kg/L etc.)
Densities of Some Common
Substances
Indiana Jones Movie Example
• In the movie, Jones replaces a gold statue with sand in
order to avoid setting off a deadly booby trap
• The density of gold = 19.32 kg/L and the density of
sand = about 3 kg/L
• If the same volume of sand is used to replace the statue,
will the booby trap be set off?
• Yes, gold is around 7 times as dense as sand, so you
would have to use around 7 times the volume
• If the volume of the idol is 1.0 L (the idol is solid gold),
what is its mass (in kg and in lb)? (1 kg = 2.20 lb)
m = dV = (19.32 kg/L) x (1.0 L) = 19 kg
19 kg x 2.20 lb/1 kg = 43 lb
Density from Water Displacement Method
• When fully submerged, a solid object will displace its
volume in water
• Volume of the water is measured before and after
submerging the object
- the volume difference = the volume of the object
- the mass is measured and d = m/V