Système International d'Unités S.I. Units

A scratch: Marie Antoinette on the Guillotine, October 16, 1793

Throughout history people have tried to develop units of measurement so that they could communicate quantities to one another in some definable amount. The problem with these systems was that every country had its own defined measurements that may or may not be compatible with another country’s system. The acre, for instance, was the area a team of oxen could plow in one day. In England this was 43,650 ft2. In Scotland, 54,885 ft2 and in Ireland, 70,567 ft2. Apparently English Oxen were not as good at plowing as their neighbors. If you lived in the Southwest United States you might measure land using varas, the length of one pace of a donkey, or about 33 1/3 inches. This system is not used much today for two reasons. First, because it is very difficult to get a donkey to keep track of its paces and second, because donkeys do not always want to measure the same things we would like them to. In about 1795, near the end of the French Revolution, the French, tired of the old argument about whose oxen could plow the most land, decided to fix the problem. They developed the Metric System. A system based on units of ten. The first thing they did was develop a unit for length, the meter. It was defined as 1/10,000,000 (one ten millionth) the distance from the equator to the North Pole. In 1983 the CGPM, General Conference on Weights and Measures, this is a bunch of people who decide what is and is not proper measurement decorum, replaced this former definition by the following definition: The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. This new definition is a lot easier to reproduce than having someone measure the distance from the equator to the North Pole. Today, we use SI or, International System of Units (Système International d'Unités in French) This is a system of units developed by the CGPM. There are seven basic SI units. They are, UNIT

NAME

SYMBOL

length mass time electric current thermodynamic temperature amount of substance luminous intensity

metre (meter) kilogram second ampere kelvin mole candela

m kg s A K mol cd

All other units can be derived from these seven. Some of this information is not vital to your passing this course. What is important is that you be able to convert within the SI system. In order to do this, you will need to know some basic information. The SI system is based on a unit of ten. Each base ten unit has a name, which is known as a prefix. Some prefixes are listed in the following table.

Amore/Kosmas/Lovins/Moskaluk

Factor 1024 1021 1018 1015 1012 109 106 103 102 101

Name yotta zetta exa peta tera giga mega kilo hecto deka

Symbol Y Z E P T G M k h da

Factor 10-1 10-2 10-3 10-6 10-9 10-12 10-15 10-18 10-21 10-24

Name deci centi milli micro nano pico femto atto zepto yocto

Symbol d c m µ n p f a z y

To convert within this system, we must remember that each prefix is ten (10) or some multiple of 10 times larger or smaller that the units before or after it. To do these conversions we will use what is called Dimensional Analysis, a fancy term meaning “Easy way to convert stuff” I know you are all used to Kangaroos hopping ditches, but dimensional analysis can be used to convert anything and the kangaroos can’t. Let us suppose that we need to convert 30 cm to meters. First

Write down the term that we want to convert

30 cm

Second

We need to write out the conversion factor. This can be obtained from our list of prefixes.

0.01 m = 1cm

Third

Make a fraction out of the conversion factor

1cm 0.01m or These fractions 0.01m 1cm mean the same thing. Both equal 1

Fourth

This is the tricky part. 1) Write out the term to be converted 2) Choose one of our conversion fractions. (see step 3) a) To determine which fraction to choose, look at what we want to convert. In this case, cm. b) Choose the fraction that has this unit in its denominator 3) Multiply the term to be converted by the fraction

In this example you will notice that centimeters cancel out leaving meters. Now you do one. Convert 45 km to cm Amore/Kosmas/Lovins/Moskaluk

1) 30 cm

2)

0 . 01 m 1cm

Note, cm is in the denominator.

3) 30cm ×

0.01m = 0.3m 1cm

Remember the steps: First

Second

Third

Fourth

Did you get 4,500,000? 0.00001 km = 1cm

45km ×

1cm = 4,500,000cm (Note, km is in the denominator) 0.00001km

I know you are still thinking that the kangaroos can do this. They can, but they cannot convert 358 cubits to centimeters. Dimensional Analysis can!! All we need to know, is that 1 cubit = 45.72 cm. First

358 cubits

Second

1 cubit = 45.72 cm

Third

1cubit 45.72cm or 45.72cm 1cubit

Fourth

358cubits ×

45.72cm = 16367.76cm (Again, notice that cubits is in the denominator) 1cubit

Dimensional Analysis is the method we will use to do all of our converting in this class. Start using dimensional analysis now and it will become much easier to work out the problems. Fail to practice dimensional analysis now and all there is left to look forward to is utter darkness and gnashing of teeth.

Amore/Kosmas/Lovins/Moskaluk