# measurement and problem solving

```Scientific Method
The scientific method is a logical
approach to solving problems by
observing and collecting data,
formulating hypotheses, testing
hypotheses, and formulating theories that
are supported by data.
I. Qualitative vs.
Quantitative
Measurements
Qualitative Measurement
1). Qualitative measurement = a measurement
that gives descriptive, NONnumeric results
a) Ex: Jillian ran a fast race.
b) Ex: The light was green
Quantitative Measurement
2) Quantitative measurement = a measurement
that gives results in definite form, usually in
numbers and units
a) Ex: Jeff finished his race in 54.3 seconds
b) Ex: the light had a wavelength of 505
nanometers.
Variables
Independent variables
Dependent variables
Control variables
II. “SI” System
1) SI System = a modernized form of the metric
system used by scientists
A. Fundamental SI Units
1) Fundamental unit = a unit that is defined by a
single standard of measurement
Fundamental SI Units
(There are seven fundamental SI units)
A. Fundamental SI Units
3) Length = a measure of linear distance;
the fundamental SI unit of length is the
meter (m)
a) The distance light travels in a
vacuum
during a time interval of
1/299792458 of a second is the SI
standard for one meter
A. Fundamental SI Units
4) Mass = a measure of the quantity of matter in
a sample; the fundamental SI unit of mass is the
kilogram (kg); the abbreviation for gram is “g”
a) A platinum-iridium cylinder kept at the
International Bureau of Weights and
Measures in the French town of Sevres is
the SI standard for one kilogram
A. Fundamental SI Units
b) Weight = a measure of the gravitational pull on
matter
A. Fundamental SI Units
5) Time = a measure of the interval between
occurrences; the fundamental SI unit of time is
the second (s)
a) The duration of 9,192,631,770 periods of
atoms is the SI standard for one second.
B. Derived Unit
1) Derived unit = a unit that can be obtained from
combinations of fundamental units
Examples of Derived SI Units
B. Derived Unit
3) Volume = a measure of the amount of space
occupied by a sample of matter; the derived SI
unit of volume is the cubic meter (m3)
a) Chemists often use a non-SI unit for
volume, the liter (L)
b) 1 dm3 = 1 L
c) 1 cm3 = 1mL
C. Prefixes
1) Other SI units are obtained by combining
prefixes with a root unit. The prefixes represent
multiples or fractions of 10. The following table
lists some prefixes:
Prefixes Used with SI Units
D. Prefixes Used with SI Units
Write the correct abbreviation
for each of the following units.
a) Kilosecond ______________
ks
hg
b) Hectogram ______________
daL
c) Dekaliter _______________
dL
d) Deciliter ______________
cm
e) Centimeter _______________
mg
f) Milligram ______________
E. Conversions
Try these conversions, using the
1.0
a) 1000 mg = ___________
g
1,600
b) 160 cm = ____________
mm
0.109
c) 109 g = _____________
kg
1,000
d) 1 L = _____________
mL
14,000
e) 14 km = _____________
m
0.250
f) 250 m = ______________
km
F. Other Useful Conversions
1) Some English System Conversions (exact conversions):
1 foot (ft) = 12 inches (in)
1 pound (lb) = 16 ounces (oz)
1 yard (yd) = 3 feet (ft)
1 ton = 2000 pounds (lb)
1 mile (mi) = 5280 feet (ft)
1 quart (qt) = 32 fluid ounces (fl oz)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 4 quarts (qt)
2) Some conversions between systems:
1 inch (in) = 2.54 centimeters (cm)
1 pound (lb) = 453.59 grams (g)
1 gallon (gal) = 3.7854 liters (L)
III. Scientific
Notation
1) 4.6 x 103 m =
4.6 m x 10 x 10 x 10 =
4600 m
2) 5.4 x 10-3 m =
5.4 m &divide; 10 &divide; 10 &divide; 10 =
0.0054 m
3) For numbers expressed in scientific
notation, the decimal place goes after
the first nonzero digit.
4) Write each of the following
numbers in scientific notation.
-4 g
3.47
x
10
a) 0.000347 g = ________________
5 km
2.89302
x
10
b) 289,302 km = ________________
-5 mm
4.477
x
10
c) 0.00004477 mm = _______________
5) Write each of the following
numbers in ordinary notation.
89,500 m
a) 8.95 x 104 m = _________________
0.00004796 hm
b) 4.796 x 10-5 hm = _______________
273,000 cm
c) 2.73 x 105 cm = _________________
Significant Figures
IV. Taking Measurements
1) Review the proper way to measure
thermometer, etc.
IV. Taking Measurements
Meniscus = the curvature of a liquid in a
container because of surface tension.
Your eye should be level with the top of
the liquid and you should read the bottom
of the meniscus.
V. Precision, Accuracy and
Percent Error:
1) Precision = a measure of how close a
series of measurements are to one
another
a) It takes a series of measurements to
determine precision
V. Precision, Accuracy and
Percent Error:
2) Accuracy = a measure of how close a
measurement comes to the true or accepted value
of what is measured
3) Bull’s Eye Analogy
V. Precision, Accuracy and
Percent Error:
4) Percent error = the difference between the
measured quantity and the accepted value,
expressed as a percentage of the accepted value
Percent Error Formula:
Value accepted - Valueexperimental
% error =
Value accepted
x 100
5) Gary measured the density of a piece of lead to be
12.12 g/cm3. The accepted value for the density of lead
is 11.35 g/cm3. Calculate the percent error.
VI. Problem Solving
1) Approach to solving problems
a) Analyze:
1) Read the problem carefully at least
twice.
2) Identify what you know and what
you are trying to find.
3) Include units.
VI. Problem Solving
b) Plan:
1) Graphs, pictures, graphic organizers,
flowcharts, or other visual aids
2) Identify formulas and/or conversion
factors that will be used.
3) Be certain that “units will cancel” as
needed.
4) Solve formulas for an unknown
variable before putting in values.
5) Set-up the problem
VI. Problem Solving
c) Compute:
1) Plug in given information, conversion
factors, and other necessary values. Include
units on all numbers!!
2) Cancel units properly.
VI. Problem Solving
d) Evaluate:
2) Is the same answer obtained after
rechecking?
3) Do the units cancel correctly so the
4) Have all parts of the question be
VII. Density:
1) What is heavier, a pound of lead or a
pound of cork?
Neither, they both weigh a pound!!!
VII. Density:
2) What floats in water, lead or cork? Why?
Cork floats in water because it is LESS
dense than water
VII. Density:
Take a look at the two boxes below. Each
box has the same volume. If each ball has
the same mass, which box would weigh more?
Why?
VII. Density:
The box that has more balls has more
mass per unit of volume.
This property of matter is called
DENSITY.
VII. Density:
4) Density = a property of
matter representing the mass per
unit volume.
a) The derived SI unit of
density: kg/m3
b) Other commonly used
density units, g/cm3, g/mL,
g/L
VII. Density:
c) Volumes can change with temperature,
therefore, densities also change with
temperature.
Ex: Increasing the temperature of a
gas would also increase the volume of the
gas. Therefore the temperature of the gas,
affects the density of the gas!
VII. Density:
d) Formula:
Density =
Mass__
Volume
Or
D=M
V
VII. Density:
5) Solve the density formula for mass.
VII. Density:
6) Solve the density formula for volume.
7) A sample of aluminum metal has a mass of
8.4g. The volume of the sample is 3.1cm3.
Calculate the density of aluminum.
8) Diamond has a density of 3.26 g/cm3. What is
the mass of a 0.350 cm3 of diamond?
9) Suppose a scientist collects 76.2g of mercury.
Calculate the volume given that the density of
mercury is 13.6 g/mL.
```