The original intent of the metric system is to have one name for each characteristic to be measured. For example, the only unit of distance is the meter. That characteristic could then be magnified or diminished with an appropriate prefix. For example, ‘deci’ means a tenth so that a decimeter is one tenth of a meter.

The next important thing is to relate the different characteristics by defining their corresponding units so that fudge factors are not needed. The unit of volute is called liter and is defined as a cubic decimeter. The unit of mass is called kilogram as defined by the international prototype. The unit of time is called second. The unit of force is called the newton. So if I say ‘F=ma’, the unit of force was chosen so that it requires a force of one newton to accelerate a mass of one kilogram at a rate of one meter per second every second. The energy needed to push an object with a force of one newton for a distance of one meter is one joule. The power needed to push an object with a force of one newton at a velocity of one meter per second is one watt. In the design of the metric system, great effort was made to avoid fudge factors.

The metric system was designed to be easy to understand. For each characteristic to be measured [except mass], only one unit is defined. And that unit can be scaled from the very small to the very large. Units for derived characteristics are defined so that fudge factors are not needed. It is for these reasons that we should use the metric system that is the official United States system of weights and measure. Metric units define non-metric units of weights and measure used in the United States.

Basic Unit Definitions

The standard measurement of length in the United States is the meter (m). What the meter is has been redefined many times. In 1799 the meter was originally defined as one ten millionth of the quadrant of the earth through Paris. Later in 1872, thirty prototype meters were made on metal bars with marks to indicate the meter. In 1960 the meter was redefined as 1650763.73 wavelengths of the orange-red line of krypton-86. And in 1983 the meter was again redefined so that the speed of light in a vacuum was exactly 299729458 meters/second.

In 1964, a liter [L or l] was defined as one cubic decimeter.

The kilogram (kg) is the unit of mass and is equal to the mass of the international prototype of the kilogram. One liter of water at maximum density, about 4 degrees Celsius, standard pressure, has a mass very close to 1 kilogram.

The second is the unit of time.

Next I need to describe metric notation and derived metric units. Since the metric system uses Greek and special characters, and the explanation of prefixes uses exponentiation, it is necessary for you to please go to a remote page and return when done.

Relationships between Metric Units

By design, metric units combine to form new units to measure other properties. The following table may prove useful. For all practical purposes:

Volume Volume Mass of Water

cubic meter kiloliter metric ton [megagram]

cubic decimeter liter kilogram

cubic centimeter milliliter gram

cubic millimeter microliter milligram

It shows the relationship between volume expressed in cubic meters, and the equivalent volume in liters, and the mass of water, at maximum density, which is about 4 degrees centigrade that will fill that volume. Note that water therefore has a maximum density of about 1 metric ton per cubic meter [kiloliter], and 1 kilogram per liter, and 1 gram per milliliter, and 1 milligram per microliter.

Similarly, the unit of pressure is called a pascal and is a newton per square meter, and is equal to a centinewton per square decimeter, and is equal to 100 micronewtons per square centimeter, and is equal to a micronewton per square millimeter.

Algebra on Units

A measurement consists of two parts, the number and the unit. Both are important. If I were to say:

9.806650 = 32.17405 = 21.93685

you would say I was wrong. And I would be wrong. But if I were to say:

1 G = 9.806650 m/sec2 = 32.17405 ft/sec2 = 21.93685 mph/sec

Then I would be right. [More or less, these are approximations] Note that here “G” represents the standard [average] acceleration of a mass on the surface of the Earth due to the force of gravity.

If I multiply 30 cm. by 40 cm., the answer is 1200 square cm. Note that the units are subject to the same algebraic manipulation as are the numbers. Acceleration is the rate of change of velocity. Rate of change, also known as a time derivative, has the unit 1/sec. Distance is the area under the velocity versus time plot. This area, also known as a time integral, has the unit sec. Thus the rate of change of distance with time is velocity, the rate of change of velocity is acceleration, and the rate of change of acceleration is jerk. If the distance is in meters and the time in seconds, the corresponding units are:

Distance in meters

Velocity in meters per second

Acceleration in meters per second squared

Jerk in meters per second cubed

Velocity will always be in the form of unit distance per unit time. Any other unit is wrong. Knowing how to multiply and divide units is essential to understanding science.

Metric Review

To summarize, the basic units of the Metric System are the meter [m], kilogram [kg] and the second [s]. 100 inches is the same distance as 2.54 meters. A cubic decimeter [0.1 m or about 3.937 inches on a side] is a liter [l]. Fill that liter with cold water and the water will have a mass very close to a kilogram [kg]. In Saint Louis, Missouri, that kilogram will have a weight of about 9.8 Newtons [N]. Raise that kilogram up 1 meter and you will have done 9.8 joules [J] of work. To raise that kilogram up 1 meter in 1 second requires a power of 9.8 watts [W]. The pressure at the bottom of that cubic decimeter of water is 0.98 kilopascal [kPa]

Weight of 100 kg [220.46223 lbm.] (as a function of location)

North Pole 983.217 N 221.036 lbf.

St. Michael, Alaska 982.192 N 220.806 lbf.

Paris, France 980.943 N 220.525 lbf.

Standard Gravity 980.665 N 220.46223 lbf. (avoirdupois)

New York, New York 980.267 N 220.373 lbf.

Key West, Florida 978.970 N 220.081 lbf.

Equator 978.039 N 219.872 lbf.

Surface of Mars 369.7 N 83.1 lbf.

Surface of our Moon 162.7 N 36.5 lbf.

Surface of Pluto 65.7 N 14.7 lbf.

Mass & Weight are not the same thing. The weight of an object varies with location. But its mass remains the same wherever it is. The mass of an object is measured on a balance scale by comparing it with other masses. Weight is a force and must be measured on a spring scale. The chart above shows how the weight of a 100 kg mass changes with location. Weight even changes with time of day. In the United States, things weigh the least at noon, in June, with a new moon! The difference is not much, but it is enough to cause the tides.

Note that when selling sugar, apples, nuts, etc., 1 lb = .45359237 kg. At the standard gravity of 9.80665 meters per second squared, a one pound mass has a weight of one pound force.

History

1790 Thomas Jefferson proposed a decimal-based system of measurement for the United States. France’s Louis XVI authorized scientific investigations aimed at a reform of French weights and measures. This led to the development of the first “metric” system.

1792 The U.S. Mint was formed to produce decimal currency. (the U.S. dollar consisting of 100 cents). $25 was then defined as the worth of 1 oz. of gold.

1795 France officially adopted the metric system.

1866 Congress authorized the use of the metric system in the United States and gave each state a set of standard metric weights and measures.

1875 United states became one of the original 17 signatory nations to the Treaty of the Meter.

1893 United States adopted fundamental metric standards for length and mass.

1958 U.S. and imperial yards were adjusted to metric measurement. I.e. the U.S. inch was shortened to exactly 2.54 cm.

1960 The International System of Units, abbreviated SI, was approved by the General Conference of Weights and Measures.

1985 Congress passed the Metric Conversion Act of 1975. The Metric Board was established.

1982 The Metric Board was dissolved.

1988 Congress passed the Omnibus Trade and Competitiveness Act of 1988. Designated the metric system as the preferred system of weights and measures for United States trade and commerce.

Refereces

U.S. Metric Association: [http://www.metric.org]

National Institute of Standards and Technology: [http://ts.nist.gov/WeightsAndMeasures/Publications/appxc.cfm]

Learning the Metric System

The best way to learn the metric system is to see and feel familiar things that have a metric label. Many of us grew up using 35 mm film with a width of 3.5 cm. The standard CD is 12 cm in diameter. Buy a meter stick and use it. The mass of a 1000 mg tablet of aspirin is 1 g. Buy a liter of bottled water and know that the bottle has a volume of 1 cubic decimeter and a mass of about 1 kg. Two and a half laps around your local high school football field [5 furlongs] is just over 1 km. Tires on a small car often will have a maximum inflation pressure of 300 kPa. Water freezes at 0 degrees Celsius and boils at 100 degrees Celsius at sea-level atmospheric pressure. That pressure will support a column of mercury about 76 cm high. Music of a marching band has a 2 Hz beat. In the United States music, the ‘A’ above middle ‘C’ has a frequency of 440 Hz. If your energy bill says your average energy use was 720 kW-hr/month [30 day month], that was an average power of 1 kW, the power of ten 100 W light bulbs, about the power of bright sunlight on one square meter that is perpendicular to the sun and at the Earth’s surface. A kW-hr of energy is 3.6 MJ. Light will travel almost 30 cm in a ns [nanosecond].

Think Metric!