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Units, Scientific Notation, and Significant Figures

Units

Terms and Definitions

Problems

Defining Units

When trying to describe the quantity or quality of something, whether a chemical substance or physical phenomenon, it is helpful to have some standard measure to refer to. A unit is nothing more than a standard by which a measured value can be described. For instance, in the old English system, a foot was just that--the length of a man's foot. This was helpful in that when a distance between, say, a house and a water well was described in feet, one who had never seen the dwelling in question would have an instant idea of how far away the well was, based solely on a verbal description. The concept today hasn't changed, although our standards make better scientific sense and are more exact.

Systems of Units

There are two different sets of units used in scientific measurements: British Engineering units and the metric system (also called the Standard International (SI) system). Both are based on standards, though those underlying the British system can be shockingly inscrutable. The metric system is based on a far less arbitrary system of tens, and is far more rational, intelligent, and easier to use. In general, people tend to stick with the system with which they are most familiar, and have the most intuitive feeling for. The United States uses the British system; most of the rest of the world (including Britain) uses the metric system. In terms of science, the metric system is almost always used. For Americans, it is therefore often necessary to make conversions between the two. Conversion tables reside in the "Reference" pull-down menu at the top of most SparkNotes pages.

Metric Units (SI units)

The standards metric terms for commonly measured characteristics are listed in below.

Property Unit Symbol
Mass kilograms kg
Length meters m
Volume liters L
Time seconds s
Electric Current ampere A
Temperature Kelvin, Celsius K, C
Intensity of light candela cd
Amount of a Substance mole mol

Temperature in the table above is expressed in both Kelvin (K) and Celsius (C). One kelvin is exactly the same as one C, except that the Kelvin scale starts at absolute zero, or -273.15 C, the lowest temperature possible, instead of the freezing point of water. Therefore water freezes at 273.15 K or 0 C.

Prefixes for Units

In addition to the basic metric units described above, there are prefixes to indicate larger or smaller quantities. For example, a meter refers to a standard metric measure of length. A millimeter refers to a measure that is one thousandth the size of a meter (one thousand millimeters fit into a meter); a kilometer refers to a distance one thousand times longer than a meter (one thousand meters fit into a kilometer). By wisely using these prefixes, you can avoid having to use huge numbers or having to resort to scientific notation. The table below shows the most commonly encountered prefixes:

Prefix Symbol Value Description
pico p 10-12 1 picoliter, (pL) = 0.000000000001 l
nano n 10-9 1 nanogram, (ng) = 0.0000000001 g
micro µ or u 10-6 1 micrometer (µm) = 0.000001 m
milli m 10-3 1 milliliter (mL) = 0.001 L
centi c 10-2 1 centimeter (cm) = 0.01 m
deci d 10-1 1 decigram (dg) = 0.1 g
none none 1 normal units without prefixes
kilo k 103 1 kilogram (kg) = 1000 g
mega M 106 1 megagram (Mg) = 1,000,000 g
giga G 109 1 gigameter (Gm) = 1,000,000,000 m
tera T 1012 1 teraliter (TL) = 1,000,000,000,000 L

Using Units (Dimensional Analysis)

In working out calculations, units can provide an excellent source of self-correction. When you perform a calculation in any science, you will almsot always be looking not just for a number, but for a number of a specific type of unit. If the answer your work yields does not have the correct units, then you know you have made a mistake somewhere.

For instance, lets say that a person who weighs 150 lbs (a British system measurement) wants to know her weight in kilograms (a metric system measurement). Start by drawing a horizontal line, and then making vertical hash marks to form a table as in step one of the figure below.

Figure %: Units in calculations

The woman knows her weight in pounds and wants to find out what she weighs in kilograms. As seen in step two, she should enter the known weight in pounds next to the ratio of pounds to kilograms (1 : 2.205) in such a way that the units cancel one another. This means that if lbs are on top, then there must be lbs on the bottom, so that when they are divided, they cancel. Next, while carrying out the obvious mathematical operation, cancel the units. If the woman had accidentally put the ratio of pounds to kilograms in upside down (2.205 : 1), then the units would not have canceled out, alerting the woman that she had made a mistake.

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