Chemists measure all kinds of stuff in the laboratory. While many observations are qualitative; what color, what state, etc., many observations are quantitative. Measuring the mass of a reactant, or the volume of a liquid, performing a titration, and other more sophisticated measurements require careful determination of a value which must be recorded along with the proper unit. Both the magnitude of the number and the unit are essential for communicating information to other chemist wishing to repeat an experiment.

What are units? Units are labels that help define the nature of the measurement. For example, if we see units of grams we think mass of a sample, units of meters and we think length. Other units may be unknown to us like, joules, pascals or kelvins.

There are two types of units; base and derived. The base units are those units which are defined by scientists as a minimum set from which all other units can be derived. Not just anyone can decide on a unit. The units have been set by an international committee. There are seven base units, five of which are important to us.

SI (Systeme International) Base Units

We will not use the last two unit in this list.

Derived units are obtained by combining units by multiplying or dividing. Some common derived units include;

Derived Units

While it is unlikely I will ask you to differentiate between derived and base units you will need to recognize the unit from its symbol, and associate the appropriate physical quantity with the symbol. I'll show you what I mean in the Self-Test below.

The units listed above are those units associated with the Systeme International, or SI. This group of units are also referred to as the Metric System. In the US we use the English System of units.

In the English system we have a variety of units which are associated with the same physical quantity, but differ in magnitude. For example consider length. We use the unit inch for a short measure and the unit mile for a long measure. There are other units of length; foot, yard, span, rod, furlong, etc. In the metric system only one unit is associated with a particular physical quantity and prefixes are used to specify large or small measures. If we continue with length, the standard unit is the meter. A short unit is a centimeter, or a millimeter and a long unit is a kilometer. Centi-, milli- and kilo- are all prefixes that specify a particular multipler of the unit meter. Common prefixes are listed below;

Prefixes Used in the SI System

Prefix	Symbol	Meaning	Exponential Notation
exa	E	1,000,000,000,000,000,000	1018
peta	P	1,000,000,000,000,000	1015
tera	T	1,000,000,000,000	1012
giga	G	1,000,000,000	109
mega	M	1,000,000	106
kilo	k	1,000	103
hecto	h	100	102
deka	da	10	101
		1	100
deci	d	0.1	10-1
centi	c	0.01	10-2
milli	m	0.001	10-3
micro		0.000001	10-6
nano	n	0.000000001	10-9
pico	p	0.000000000001	10-12
femto	f	0.000000000000001	10-15
atto	a	0.000000000000000001	10-18

I want you to memorize the prefixes from nano- through giga-. You are to learn what the multiplier is in both decimal and scientific notation. Check the Self-Test to see the type of question you must be able to do.

Here are the important unit relationship for the English System of units that I'll expect you to know.

• 12 in = 1 foot 3 feet = 1 yard 5280 ft = 1 mile

  4 quarts = 1 gallon 2 pints = 1 quart

  16 ounces = 1 pound 2000 lbs = 1 ton

Coversions that will be provided:

• 1 in = 2.54 cm

  1.0567 qt = 1 L

  1 lb = 453.59 g (454 g)

When scientists perform experiments they often do not know the answer. The only way they can be confident of the result of the experiment is through repetitive experiments. Doing the same experiment and verifying the same result. When a scientist obtains agreement among several measurements of the same quantity it is called precision. The scientist having demonstrated the reproducibility of the measurement can then be confident of the accuracy of the measurement. Accuracy means the the agreement of a particular value with the true value.

Precision is also related to the scale used on a measuring device. For example, measuring length. It is easier to be precise when the measuring instrument has scale marked in very small units. A ruler marked in centimeters, with no other finer mark is less precise compared to a ruler with marks in millimeters between the centimeters. If the person reading the ruler must estimate the length between large units like centimeters the precision of the measurement will drop. Measuring length with a millimeter scale makes for more precise measures, agreement between several measurments of the same quantity. However, there is still some uncertainty in the measurement, no matter how precise the measuring device.

Here is an animation which shows the difference between accuracy and precision. (You will need the MacroMedia Shockwave plug-in for Director to view the animation. Check the plug-ins link on our homepage.)

In science most measurements are accompanied with some degree of uncertainty. Anytime we attempt to measure the mass of an object, or its length or volume there will be uncertainty in the measurement.

Here is an animation which shows how the precision of the measuring device leads to uncertainty. (You will need the MacroMedia Shockwave plug-in for Director to view the animation. Check the plug-ins link on our homepage.)

There are measurments that can have very little if any uncertainty. Counting a small number of objects can usually be done with a high degree of certainty. Such situations give rise to an exact number.

Since measurements usually have some degree of uncertainty we must have a standard way of communicating that uncertainty. So the number not only indicates the magnitude of the measurement but also the degree of uncertainty. We use the concept of significant figures to indicate the precsion of the measurment. Our textbook lists the rules for assigning significant figures as;

1. All nonzero digits are significant

2. Zeros between nonzero digits are significant

3. Zeros that precede the first nonzero digit are not significant. Reading from left to right begin counting with the first nonzero digit.

4. Zeros are significant when they appear; in the middle of a number, at the end of a number that includes a decimal point.

5. Zeros at the end of a number without a decimal point are ambiguous. We will assume they are NOT significant.

Lets try some examples to see how to apply these rules.

When performing calculations with numbers we must always be careful to report the number produced in the calculation to the correct number of significant figures. Rules for determining significant figures in calculations are the same for multiplication and division, but the rules for multplying and dividing are different when compared to addition and subtraction. When writing the result to the correct number of significant figure rounding is almost always required and there are specific rules for rounding off numbers.

When multiplying and dividing measured quantities, there should be as many significant figures in the answer as there are in the measurement with the least number of significant figures.

When adding or subtracting measured quantities, there should be the same number of decimal places in the answer as there are in the measurement with the least number of decimal places. For addition and subtraction the number of significant figures is NOT important.

Look at the left most digit to be dropped

• If this digit is '5' or greater, or is '5' followed by nonzero digits, add '1' to the last digit to be retained and drop all the digits further to the right.

• If this digit is less than '5', drop it and all digits further to the right.

So lets try some examples where we report a calculation to the correct number of significant figures.