Chapter 2: Measurements and Calculations
I.
Scientific Method
A. Scientific Method - a logical approach to solving problems
B. A hypothesis is a testable statement or explanation.
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.
F.
Because it is characteristic of a substance, density can be used to
determine the identity of a substance.
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.
5.
Multiply/Divide: round answer to the fewest number of sig
figs.
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)