Chapter 2: Measurements and
Calculations
I. Scientific Method
A. Scientific Method - a logical approach to
solving problems
B. There are generally four steps:
1. Observing and collecting data.
a. Data can be either descriptive
(qualitative) or numerical
(quantitative).
b. Data is collected by experimenting.
c. Experiments involve studying systems.
A system is a specific portion of matter
in a given region of space that has been
selected for study during an experiment
or observation.
2. Formulating Hypotheses.
- A hypothesis is a testable statement
or explanation.
3. Testing Hypotheses.
a. Requires experimentation that either
proves or disproves the hypothesis.
b. If the hypothesis is proved move onto
the next step.
c. If the hypothesis is disproved, return
to step 2.
4. Theorizing.
a. Explaining the phenomena being
studied by constructing a model.
b. The results are then published, and
sent to other scientists.
II. Units of Measurement
A. SI Measurement
1. Data can be either descriptive
(qualitative) or numerical (quantitative).
2. A measurement represents a quantity. A
quantity: something that has
magnitude, size, or amount.
3. The units are regulated by using the SI
system. SI is short for “Le Système
International d’Unitès”. (That’s French).
4. SI units are defined in terms of
standards of measurement.
B. SI Base Units.
1. A base unit is a unit that is 1
dimensional.
2. The SI base units are listed Table 1 on
page 34.
*Note - mass is measured in kg, it is not
a weight. Weight is a measure of the
gravitational pull on matter.
C. SI Derived Units.
1. A derived unit is a unit that is formed
by a combination of base units. It is
multidimensional.
2. The SI derived units are listed in Table 3
on page 36.
D. Prefixes.
1. SI units use prefixes in order to show
magnitude.
2. The prefixes are listed in the table given.
3. Know prefix, symbol, and magnitude of
Mega, Kilo, Deci, Centi, Milli, Micro, Nano,
and Pico.
E. Density.
1. Density - the ratio of mass to volume,
or mass divided by volume.
2. Density is a characteristic physical
property of a substance. It is a specific
value for a given substance at a given
temperature.
3. Density determines whether something
will float or not. If you have two
substances, the less dense substance will
float on the more dense substance. (For
example: ice floats on water)
4. Because it is characteristic of a
substance, density can be used to
determine the identity of a substance.
F. Conversion Factors.
1. A conversion factor is a ratio derived
from the equality between two different
units that can be used to convert from one
unit to the other.
2. Dimensional Analysis: A mathematical
technique that allows you to use units to
solve problems involving measurements.
3. To derive a conversion factor, you need
to know the relationship between the
two quantities. (For example: 1 dollar
= 4 quarters). When this relationship is
known, divide both sides by one of the
sides. The result is your conversion
factor.
III. Using Scientific Measurements.
A. Results vary with every measurement.
Therefore we have to discuss uncertainty in
measurements.
B. Accuracy vs. Precision
1. Accuracy - refers to the closeness of
measurements to the correct or
accepted value of the measured
quantity.
2. Precision - refers to the closeness of a
set of measurements to each other.
3. A dart board is the best explanation of
this. Figure 8 on page 44.
4. Percent error is calculated by
subtracting the experimental value from
the accepted value, dividing the
difference by the accepted value, and
then multiplying by 100. Negative
values are OK.
5. Error in measurement must be reflected
in the reading. Practice by reading a
ruler. This leads to significant figures.
C. Sig Figs.
1. Significant Figures for a measurement
consist of all the digits known with
certainty plus one final digit, which is
somewhat uncertain or is estimated.
2. Rules for determining the number of sig
figs in a measurement are in Table 5 on
page 47.
3. Rules for rounding to a specific number
of sig figs are in Table 6 on page 48.
4. Rules for math operations depend on the
math operation used. Do the operation,
then round to the correct place using the
rules.
a. Add/Subtract: round answer to
fewest number of places to the right
of the decimal point.
b. Multiply/Divide: round answer to
the fewest number of sig figs.
5. When using conversion factors round the
same number of sig figs as are in the
original number.
D. Scientific Notation.
1. In order to use numbers that are really
large or really small we use scientific
notation.
2. The form is M * 10n. M is determined by
writing all of the sig figs in order, then
place the decimal point so that the
number is between 1 and 10. n is
determined by counting the number of
places that the decimal point is moved.
If you moved it to the left n is +. If
moved to the right n is -.
3. When adding or subtracting the
operation can only be performed only if
the value of n is the same. If they are
not, make them the same.
4. When multiplying, perform the operation
on both M values and then add the n
values.
5. When dividing, perform the operation on
both M values and then subtract the n
values.
E. Proportionality
1. Two quantities are directly
proportional to each other if dividing
one by the other gives a constant value.
This graph would be a straight line.
(y=mx+b)
2. Two quantities are inversely
proportional to each other if their
product is constant. This graph would
be a hyperbola. (y 1/x)