# Metric System

### Objectives

1. Recognize and use the units of the metric system for length, mass, volume.
2. Convert between the metric and the English systems for length, mass, volume.
3. Write numerical quantities with the correct number of significant figures and units.
4. Manipulate units algebraically and make unit conversions using MKS, FPS, and CGS systems.
 This section addresses, in whole or in part, the following Georgia GPS standard(s): S6CS3b. Use metric input units in scientific calculations to determine the proper unit for expressing the answer. S6CS4. Students will use tools and instruments for observing, measuring, and manipulating equipment and materials in scientific activities.

 This section addresses, in whole or in part, the following Benchmarks for Scientific Literacy: Technology is essential to science for such purposes as access to outer space and other remote locations, sample collection and treatment, measurement, data collection and storage, computation, and communication of information. When people care about what is being counted or measured, it is important for them to say what the units are (three degrees Fahrenheit is different from three centimeters, three miles from three miles per hour). Measurements are always likely to give slightly different numbers, even if what is being measured stays the same. Determine what unit (such as seconds, square inches, or dollars per tankful) an answer should be expressed in from the units of the inputs to the calculation, and be able to convert compound units (such as yen per dollar into dollar per yen, or miles per hour into feet per second). Use calculators to compare amounts proportionally. Read analog and digital meters on instruments used to make direct measurements of length, volume, weight, elapsed time, rates, and temperature, and choose appropriate units for reporting various magnitudes.

 This section addresses, in whole or in part, the following National Science Education Standards: Objects have many observable properties, including size, weight, shape, color, temperature, and the ability to react with other substances. Those properties can be measured using tools, such as rulers, balances, and thermometers. Tools help scientists make better observations, measurements, and equipment for investigations. They help scientists see, measure, and do things that they could not otherwise see, measure, and do. Mathematics is important in all aspects of scientific inquiry. Technology used to gather data enhances accuracy and allows scientists to analyze and quantify results of investigations. Science and technology are reciprocal. Science helps drive technology, as it addresses questions that demand more sophisticated instruments and provides principles for better instrumentation and technique. Technology is essential to science, because it provides instruments and techniques that enable observations of objects and phenomena that are otherwise unobservable due to factors such as quantity, distance, location, size, and speed. Technology also provides tools for investigations, inquiry, and analysis. Simple instruments, such as magnifiers, thermometers, and rulers, provide more information than scientists obtain using only their senses.[

## The Metric System

The two measurement systems generally in use in the US are the English system and the metric system. The metric system, officially called the Système International d'Unites (SI), or the International System of Units, is the system of measurement used in science.

Length, mass (or weight), and temperature can be measured using several different types of units. The two measurement systems generally in use are the English System and the Metric System.

The English System uses the foot, the pound, and the Fahrenheit (°F) scale. The Metric System uses the meter, the kilogram, and the Kelvin scale, although we more commonly use the Celsius (°C) scale.

Most of us grew up in the United States using the English System, so why change? Metrification is important because nearly all world trade involves metric goods. Presently, the U.S. is out of step with the rest of the world. This compromises our international competitiveness and limits markets for American-made products. There are only two other countries in the world (as of 1990) that do not use metric measurements. Any guesses which ones? No, not England, not France, not Canada, not Mexico. If you guessed any countries other than Liberia and South Yemen, you would be wrong. Surprised?

All of us are already familiar with at least some metric measurements: 2 liter soda bottles, 35 millimeter film, 10K (kilometer) fun runs, etc. Can you think of any others? Many cars are already built with speedometers in both miles per hour and kilometers per hour. And many products are sold with their weight in both ounces and grams.

For temperature, the Fahrenheit scale has an seemingly arbitrary basis in which water freezes at 32°F and boils at 212°F. With the Celsius scale, things are much easier to remember. Water freezes at 0°C and boils at 100°C. More useful, room temperature is approximately 72°F or 23°C, and a hot day is about 100°F or 37°C.

[Another temperature scale is sometimes used in science, the Kelvin scale, in which freezing and boiling of water are also separated by 100 degrees, but at 273 K and 373 K. This scale is sometimes called the absolute scale because it is based on absolute zero, the temperature at which molecular motions cease.
Absolute zero = O K = -273°C = -459°F.
The degree sign is not used with K because the temperature units are called Kelvins, not degrees Kelvin.]

Learning to use the Metric System should not be difficult for us. Remember that even illiterate street vendors in other countries use and understand the metric system. It is really a lot easier than the English System because everything works on groups of ten (instead of 12 inches to a foot, 3 feet to a yard, 5280 feet to a mile).

### Equivalencies

• 10 millimeters = 1 centimeter
• 100 centimeters = 1 meter
• 1000 meters = 1 kilometer

### Prefixes

• mega = a million times
• kilo = a thousand times
• hecto = a hundred times (not frequently used)
• deca = ten times (not frequently used)
• deci = one tenth (1/10) (not frequently used)
• centi = a hundredth (1/100)
• milli = a thousandth (1/1000)
• micro = a millionth (1/1,000,000)

You can remember most of this with the mnemonic "King Hector died drinking chocolate milk".

Using the prefixes, we can recognize that there are 1000 millimeters in a meter, 100 centimeters in a meter, 10 decimeters in a meter, and 1000 meters in a kilometer.

The abbreviations for the various units are written in lower case letters (not capitals), and can be found in the appendix to your book.

Just about the only thing you have to learn is approximately how large the various units are, so that you have some frame of reference.

### Length

The basic unit of length in the metric system is the meter. A meter is a little more than a yard (actually 39.370113 inches). A meter can be divided into 10 units called decimeters (not commonly used), 100 units called centimeters, and 1000 units called millimeters.

A centimeter (cm) is a little less than half an inch (0.3937 inch). One inch is equal to 2.54 cm.

There are 10 millimeters in a centimeter. A millimeter (mm) is about the size of the ball in a ball-point pen.

The kilometer is used for measuring larger distances. A kilometer is a little more than half a mile (0.62137 mile = 1 km). There are 1.6093 kilometers in a mile.

### Mass

The basic unit of mass in the metric system is the kilogram. A kilogram is a little more than 2 pounds (2.205 pounds = 1 kg).

There are 1000 grams in a kilogram. A gram is much less than an ounce. It is approximately the weight of a paperclip or a raisin. One gram is only 0.035 ounce. There are 28.35 grams in an ounce.

### Volume

The metric unit of volume, the liter, is equal to the volume of a cube with edges that are each 1/10 m long. A liter is a little more than one quart (1.06 quart = 1 liter and 1 quart = 0.95 liter).

Measurement of smaller volumes is typically in milliliters. One milliliter is the volume of one cubic centimeter (a cube with sides each equal to one centimeter). There are 1000 milliliters (ml) in a liter. One cup in the English system is approximately 250 ml, one tablespoon is approximately 15 ml, and one teaspoon is approximately 5 ml.

### Temperature

The metric unit of temperature is the kelvin (K). The temperature of an object depends on how fast the atoms and molecules which make up the object can vibrate. As the temperature drops, the vibrations of the molecules become slower. Eventually a point is reached at which molecular vibrations should cease, and this is called absolute zero. Absolute zero is the zero point on the kelvin scale (0 K). Absolute zero is -273.15°C (or -459°F).

The kelvin is written without a degree sign because the temperature units are not degrees kelvin, they are called kelvins. The symbol for kelvin is written as an uppercase letter (K). Temperatures in kelvin can only be positive and so they require no sign. The temperature scale is named after the British mathematician and physicist William Thomson Kelvin.

In the science laboratory, temperature is most commonly measured using the Celsius scale, although it is not part of the SI. The size of a degree in Celsius is identical to the size a degree in Kelvin.

Conversion factors between temperatures in degrees Fahrenheit (°F), degrees Celsius (°C), and kelvins are:

temperature (°C) + 273.15 = temperature (K)

((temperature (°F) - 32) x 5/9) = temperature (°C)

((temperature (°F) - 32) x 5/9) + 273.15 = temperature (K)

### Comparisons

• 1 gram is about the weight of a paperclip or a raisin.
• 1 kilogram is a little more than 2 pounds.
• 1 liter is a little more than a quart.
• 1 kilometer is a little more than half a mile.
• 1 meter is a little more than a yard.
• 1 centimeter is a little less than half an inch.
• 1 millimeter is about the size of the ball in a ball point pen, or the width of a pencil point.

Fundamental Units of Measure

Metric system or SI

Under the SI or International System of Units, the fundamental unit of length is meter, the fundamental unit of mass is kilogram, the fundamental unit of time is second, the fundamental unit of electric current is ampere, the fundamental unit of temperature is kelvin, the fundamental unit of luminous intensity is candela, and the fundamental unit of amount of substance is mole. These seven units are base units or fundamental units. Units of all other physical quantities are expressed in terms of these fundamental units. These base units can be defined as follows:

Meter
The distance traveled by light in a vacuum in 1/299,792,458 of a second.

Kilogram
The mass of platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris.

Second
The time taken by 9,192,631,770 vibrations of a specified wavelength of light emitted by a cesium-133 atom.

Ampere
The current that produces a magnetic force of 2x10-7 N/m per unit length, when it is passed in two long parallel wires that are 1 meter apart.

Kelvin
1/273.16 of the thermodynamic temperature of the triple point of water.

Candela
The luminous intensity, in the perpendicular direction, of a surface area of (1/600,000) m2 of a blackbody at the temperature of freezing platinum at 1 atmosphere pressure.

Mole
The amount of any substance that contains Avogadro's number NA (6.022x1023 ) atoms or molecules, which are defined as the number of carbon atoms in 12 grams of 12C.

### English System or FPS

Foot, pound and second are fundamental units of length, weight, and time under the English system or the F.P.S. system. The foot is one-third of the yard, which is now defined in terms of a meter (1 yard = 0.9144 meters). The pound is defined in terms of the gravitational attraction of the Earth at a particular place for a standard body. The second is the same as in the SI system of units.

1 yard = 3 feet = 36 inches.

1 mile = 5280 feet.

1 pound = 16 ounces.

1 gallon = 4 quarts = 8 pints.

Slug is the unit of mass under this system.

### Metric Conversions

Sometimes you need to convert from one metric unit to another metric unit, or from metric units to English units, and vice versa.

In order to perform conversions, you need a conversion factor. You may use a conversion chart in a book or online.

If you were converting 60 inches to feet, you would need to know how many inches make up a foot. That would be your conversion factor. You probably already know the answer: 1 foot = 12 inches. This can also be written as 1 foot/12 inches (or 1 foot divided by 12 inches). You can multiply this "conversion factor" by the 60 inches (or whatever you are asked to convert), because in math, you can always multiply something by 1 without changing anything. So you are essentially multiplying 60 inches by 1. (Because 1 foot = 12 inches, then 1 foot/12 inches = 1). You can perform the calculation as follows:

 60 inches x 1 foot = 60 ft = 5 ft ___________ ___________ ___________ 1 12 inches 12

The important thing to note about the above equation is that the units behave like numbers when you multiply fractions. Note that the unit, "inches", cancels out, and so you are left with feet (or ft). Then all you have to worry about is the numbers. This method of solving the problem is called dimensional analysis. It is ABSOLUTELY CRITICAL that you ALWAYS include all units when you set up your calculations. You have to see which units cancel to be sure that you have the correct answer.

The importance of showing all units becomes more obvious when we do a more complicated calculation.

Let's convert 5 miles into kilometers.

5 mi x 1.609 km/mi = 8.045 km

The conversion factor is 1.609 km = 1 mi. Note that the miles (mi) cancel, and you are left with kilometers (km).

But there is also another way you could do this conversion.

5 mi x 1 km/0.6214 mi = 8.046 km

In this example, we are also multiplying 5 miles by something that is equivalent to 1, but in this case we are using the conversion factor 1 km = 0.6214 mi. Note that again, the miles (mi) cancel, and you are left with kilometers.

You might also notice that the two answers are slightly different. The reason for this is that the conversion factors in the book are shortened versions of the "real" conversion factors, rounded down to fewer decimal places. If the full conversion factor with many decimal places were used, the answers would be the same.

Note that in some of these conversions, more then one step of multiplication or division may be required. For instance, to convert kilograms to ounces, you need to convert kilograms to pounds, and then convert pounds to ounces. (Remember that there are 16 ounces in a pound.) Or, you may need to convert kilometers to feet. First you might want to convert kilometers to miles, and then convert miles to feet (Remember that there are 5280 feet per mile.)

Some content from the University System of Georgia Learning Objects Repository
Science Learning Objects - PHYS 1211K-Physics I

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created April 28, 2005
Modified August 30, 2005
Modified December 21, 2006
Modified February 3, 2007