Chapter 0
Chemical Tools: Experimentation and Measurement
LEARNING OBJECTIVE SUMMARIES
1. Obtain a general understanding of the scientific method
A hypothesis is used to explain observations, and the hypothesis is used to make a prediction that can be
tested with an experiment. Observations are made throughout the experiment and the results are
analyzed. Then the hypothesis is either reworked or abandoned depending on the results of the
experiment. Hypotheses that repeatedly hold up to repeated experiment by multiple scientists are
deemed scientific theories.
2. Be able to use units to describe quantities of mass, length, temperature, volume, density, and
energy
3. Learn the common unit prefixes, including Mega, kilo, deci, centi, milli, micro, nano, pico
4. Understand both accuracy and precision, and the difference between them
Accuracy is the absence of systematic error in measurement, so that the value obtained corresponds
to the true value.
Precision refers to the agreement between multiple measurements.
Accuracy and precision are independent of one another.
5. Be able to round appropriately and determine the number of significant figures upon algebraic
manipulations
Rules for Determining Significant Figures
a. All digits except 0 are always significant
b. Zeroes in the middle of a number are like any other digit; they are always significant.
Thus, 5.602 cm has four significant figures.
c.
Zeroes at the beginning of a number are not significant; they act only to locate the decimal point.
Thus, 0.00332 g has three significant figures. (Note that
d. Zeroes at the end of a number and after the decimal point are always significant. The assumption is
that these zeroes would not be shown unless they were significant.
Thus, 23.450 K has five significant figures. (If the value were known to only four significant figures, we
would write 23.45 K.)
e.
Zeroes at the end of a number and before the decimal point may or may not be significant. We can’t
tell whether they are part of the measurement or whether they only locate the decimal point.
Thus, 41,500 m may have three, four or five significant figures.
Sig figs upon algebraic manipulation
a. Multiplication and Division
The answer to a calculation involving multiplication or division should contain the same number of
significant figures as the factor with the smallest number of significant figures in the calculation. For
example, the answer to
has three significant figures because the least precisely known factor is 5.62, which has three
significant figures.
b.
Addition and Subtraction
The rule for addition and subtraction is that the solution must have the same number of digits to the
right of the decimal point as the number in the problem with the fewest digits to the right of the
decimal point. Take for example the addition of the following four numbers:
107.3 is only accurate to the tenths place, so the final answer can also only be accurate to the tenths
place.
Rules for Rounding
a.
If the first digit you remove is less than 5, round down by dropping it and all following digits.
Thus, 5.664525 becomes 5.66 when rounded to three significant figures because the first of the
dropped digits (4) is less than 5.
b. If the first digit you remove is 5 or greater, round up by adding 1 to the digit on the left.
Thus, 5.664525 becomes 5.7 when rounded to two significant figures because the first of the
dropped digits (6) is 5 or greater.
6. Express numbers in scientific notation
The general form of scientific notation is 1.23 × 10n.
 1.23 is the coefficient representing the significant figures a number, and can be any number of
significant figures. The decimal point is always after the first significant figure.
 n is a positive or negative integer indicating the number of times the decimal point was moved
from the standard representation of the number.
7. Apply dimensional analysis to be able to determine appropriate units upon algebraic
manipulations
Dimensional analysis is the most organized way to perform unit conversions as well as many other
chemical calculations. It ensures that you’re combining the values in the appropriate way by
analyzing the units of each of the values. As long as your original units cancel and the units that are
left are what is being asked for, then the numbers are set up correctly!