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HISTORY. Man has realized for thousands of years that he must have a system of weights and measures for trade and commerce. Ancient civilizations in Egypt, Mesopotamia, and the Indus Valley developed standard weights and measures. In the 13th century, England developed standards based on the older Roman standards. In 1789, the revolutionary government of France commissioned the French Academy of Science to establish a system of measurement and weights suitable for use throughout the world. The Academy created a system that was simple and scientific. The unit of length (meter or metre) was standard-ized by marking the distance on a platinum bar. Measures for capacity (volume) and mass (weight) were derived from the unit of length, thus relating the basic units of the system to each other. Furthermore, larger and smaller versions of each unit were created by multiplying or dividing the basic unit by 10 or multiples of 10, thus making this system (called the metric system) a "base 10" or "decimal" system. In 1799, these standards were legally adopted as the weights and measures in France.

What country is credited with developing a system of measurements founded upon the powers of 10?

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The British Empire, however, did not adapt the metric system. Since the primary trading partners of the United States were Great Britain and Canada, the U.S. kept the "English" standards even though the U.S. had gone to a decimal system of coinage in 1786. In 1816, President Madison suggested going to the metric system, but the U.S. stayed with the English system.

The metric system continued to gain in acceptance throughout the world. In 1866, the metric system was made legal in the United States. Eventually, the U.S. defined its "English" units in terms of the metric system. For example, one inch is defined as being equal to exactly 2.54 centimeters.

Many scientists believed that the metric system should be based upon natural standards of even greater permanence and greater precision. In 1960, the metric system underwent revision to become the International System of Units, usually called the SI (Système International). Among the changes made was that the meter was defined in wavelengths of a certain type of light. In 1983, the meter was again redefined to improve its accuracy. Now the meter is defined as the distance light in vacuum travels in 1/299,792,458 seconds. Although the technical definition has changed, the actual length of a meter remained unchanged.

How far would light in a vacuum travel in exactly one second?

France

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Currently, the United States is the only major country in the world to use the old "English" system (now usually called the United States Customary System) instead of the SI standard. The Metric Conversion Act of 1975 passed by the United States Congress states that "the policy of the United States shall be to coordinate and plan the increasing use of the metric system in the United States." The United States continues its conversion to the metric (SI) system (liter bottles of soft drinks replacing quart bottles, car engine displacement measured in liters instead of cubic inches, etc.).

The United States Customary System units are defined based on

units.

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BASIC METRIC MEASURES. Under the United States Customary System of measurement, the inch, foot, or yard is used to measure length, the pound is used to measure weight, and the gallon is used to measure volume. In the SI or metric system, you would use meters for length, grams for mass, and liters for volume.

When using the metric system:

Length is expressed in .

Mass is expressed in .

Liquid capacity is expressed in .

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NOTE: In the remainder of this lesson, the term "metric" will be used to denote the SI system of measures.

Notice that when the U.S. system was discussed in Frame 4-4, the term "weight" was used; but when the metric system was discussed, the term "mass" was used. "Weight" measures gravity's attraction to a given object (its "heaviness"). Mass is a measure of an object's resistance to acceleration (its inertia). In other words, mass is a measure of how much matter is in the object while weight measures the force exerted by the object. For our purposes, we can say that weight and mass are the same. An object with a mass of 40 kilograms (40,000 grams), for example, will weight the same anywhere on the surface of the earth since the earth's gravity exerts the same pull. This works as long as you are dealing with the earth's gravity, but what happens if you are not? An object with a mass of 40 kilograms weighs about 88 pounds on earth. On the moon, the same object would weight about 15 pounds since the moon's gravitational pull is only one-sixth that of the earth's gravity. The object's mass, however, would remain unchanged (40 kilograms), but it would feel as heavy as a 6.7 kilogram weight on earth. In orbit around the earth, the object would be weightless (zero pounds), but still retain its mass (inertia) of 40 kilograms.

NOTE: In the U.S. system, the unit used to measure mass is the slug (about 14,594 grams).

In scientific matters, it is usually easier to speak of an object's rather than its weight since its does not change. (Einstein's theories of relativity are not considered in this subcourse.)

meters

grams

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Meter. The term "metric" comes from metre (American spelling: meter), the unit of length. This term was derived from the Greek word metron (to measure). As previously stated, a meter is defined as the distance light travels in a vacuum in one 299,792,458th of a second (about 1.1 yard).

In the metric system, the basic unit of length is the , which is a little longer than the yard of the U.S. system.

mass

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Liter. The liter is equal to the volume of a cube measuring one decimeter (1/10 of a meter) on each side. A liter is equal to about 1.06 liquid quarts.

In the metric system, the basic unit of volume is the , which is a little more than the quart of the U.S. system.

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Gram. The gram is the mass of one cubic centimeter (a cube measuring 1/100 meter on each side) of pure water at 4 degrees Celsius (about 39 degrees Fahrenheit) at sea level. This temperature is used because water has the highest concentration (density) at this temperature. Sea level ensures a stable gravitational pull and atmospheric pressure. A gram is equal to about 0.0022 pounds (about 454 grams to the pound)

In the metric system, the basic unit of mass (weight) is the , which is a little more than 1/30 of an ounce of the U.S. system.

Solution to Frame 4-7.

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PREFIXES AND ROOT WORDS. The great advantage of the metric system over the U.S. system is the metric use of root (basic) terms and standard prefixes. Meter, liter, and gram are examples of root words. They basically tell you what you are dealing with (length, volume, or weight). Prefixes (word parts that go in front) are added to the root word to denote how much.

Remember that the metric system is based on the decimal system (powers of ten). The prefix, then, denotes a power of ten. You have already come across some of these terms. In Frame 4-5, for example, the term "kilogram" was used.

In the word "kilogram," the root word (what) is and the prefix (how much) is .

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The prefix "kilo-" means "1000."

Therefore, something that weighs one kilogram weighs how many

grams?

root: gram

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Some of the metric prefixes are given below. They denote larger and larger multiples of 10.

Prefix Meaning Example

deca- 10 1 decameter equals ten meters

hecto- 100 1 hectometer equals one hundred meters

kilo- 1,000 1 kilometer equals one thousand meters

mega- 1,000,000 1 megameter equals one million meters

giga- 1,000,000,000 1 gigameter equals one billion meters

Solution to Frame 4-10.

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All of the prefixes given in Frame 4-11 are multiples of 10. The metric system also used the negative powers of 10 (fractions whose denominators are multiples of 10) to denote smaller and smaller measurements. Some of these prefixes are given below.

Prefix Meaning Example

deci- 1/10 ten decimeters equal 1 meter

centi- 1/100 one hundred centimeters equal 1 meter

milli- 1/1000 one thousand millimeters equal 1 meter

micro- 1/1,000,000 one million micrometers equal 1 meter

nano- 1/1,000,000,000 one billion nanometers equal 1 meter

How many millimeters are in 3.34 meters? _____________________

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As you can see, all that is needed to change kilometers to meters is to multiply by the number of meters in a kilometer (1000). This is done simply by moving the decimal point three places to the right. You can also convert meters to kilometers by dividing by 1000 (moving the decimal point three places to the left). Consider how simple this is compared to the U.S. Customary System. For example:

12 inches = 1 foot

3 feet = 1 yard

5.5 yards = 1 rod

40 rods = 1 furlong

8 furlongs = 1 mile

How many inches are there in one mile?

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How many centimeters are in one kilometer?

Solution to Frame 4-13.

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Originally, the meter was based on the polar circumference of the earth with the measurement going through Paris. The meter was to be one ten-millionth (1/10,000,000) of the distance from the equator to the North Pole. If the Academy's measurements were correct, the distance from the equator to the North Pole would be ten . (Hint: Refer to Frame 4-11.)

NOTE: The polar circumference of the earth is estimated to be 40,000,008 meters. The distance from the equator to the North Pole is 1/4 the polar circumference, or about 10,000,002 meters.

NOTE: The earth is not a perfect sphere. The circumference of the earth measured around the equator is around 40,075,160 meters.

100 x 1000 = 100,000 centimeters

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UNITS OF DISTANCE. In the metric system, the most commonly used measurements of distance are the meter, kilometer, centimeter, and millimeter.

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As a quick review

10 millimeters = 1 centimeter.

100 centimeters = 1 meter

1000 meters = 1 kilometer

The abbreviation for meter is "m."

The abbreviation for kilometer is "km."

The abbreviation for centimeter is "cm."

The abbreviation for millimeter is "mm."

Fill in the blanks on the following chart

Millimeters Centimeters Meters Kilometers

37 mm = = =

= 25 cm = =

= = 1.2 m =

= = = 3.3 km

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In the U.S. system, the normal units of length measurement are the inch, foot, yard, and mile. These units were defined in Frame 4-13. The approximate equivalents of these units in the metric system are given below. More exact conversion figures are given in the appendix.

1 inch = 2.5 cm = 25 mm

1 foot = 30 cm = 0.3 m

1 yard = 91 cm = 0.91 m

1 mile = 1.6 km

37 mm = 3.7 cm =

0.037m = 0.000037km

250 mm = 25 cm =

0.25 m = 0.00025 km

1200 mm = 120 cm =

1.2 m = 0.0012 km

3,300,000 mm =

330,000 cm =

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In the previous frame, you were given conversion information for changing a length measurement from the U.S. system to the metric system. The information below will help you to change lengths from the metric system to the U.S. system. More exact conversion figures are given in the appendix.

1 mm = 0.04 inches

1 cm = 0.4 inches = 0.03 feet

1 m = 1.1 yards = 3.3 feet = 39 inches

1 km = 0.62 (about 5/8) miles = 1094 yards = 3281 feet

A person runs a 1600-meter race. How far did he run in U.S. measure?

Solution to Frame 4-18.

75 cm or 3/4 (0.75) m

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Jack ran a 100-yard race while Jill ran a 100-meter race.

Who ran the longer race?

By how much?

Solution to Frame 4-19.

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FRAME 4-21.

UNITS OF VOLUME. In the metric system, the most commonly used measurements of volume (capacity) are the liter, milliliter, cubic centimeter, decaliter, and cubic meter.

A liter is equal to the volume of a cube measuring one decimeter (1/10 of a meter) on each side. The volume of a cube is found by multiplying the length of one side by itself three times (width x height x depth). Since a liter is a volume equal to 1 decimeter times 1 decimeter times 1 decimeter, a liter can also be referred to as a cubic decimeter.

depth = 1

decimeter

= 1 liter (cubic decimeter)

height = 1

decimeter

width = 1 decimeter

Since a decimeter is 1/10 of a meter, how much larger is a cubic meter than a cubic decimeter (l liter)?

(Hint: 1 meter = 10 decimeters)

depth = 10

decimeters

height = 10

decimeters

width = 10 decimeters

Solution to Frame 4-20.

Jill

about 10 yards/9 m

(100 m = 110 yards. Jill ran 110 yards

OR

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Since there are 1000 cubic decimeters in a cubic meter and a liter is equal to one cubic decimeter, a cubic meter contains liters.

Solution to Frame 4-21.

1000 (10x10x10)

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FRAME 4-23.

Ten centimeters are equal to one decimeter. How many cubic centimeters (cc) are in one cubic decimeter?

depth = 10

centimeters

= 1 cubic decimeter

height = 10

centimeters

width = 10 centimeters

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There are 1000 cubic centimeters in one cubic decimeter.

A liter equals one cubic decimeter.

A milliliter is 1/1000 of a liter (see definition of "milli-" in Frame 4-12).

Therefore, a cubic centimeter equals milliliter(s).

Solution to Frame 4-23.

1000

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A cubic centimeter is abbreviated "cc."

A liter is usually abbreviated "L."

A milliliter is usually abbreviated "mL."

NOTE: The term "liter" can also be abbreviated as a lower case letter. The upper case is used in this subcourse and elsewhere to help distinguish the letter "l" from the number "1."

A kiloliter (kL) is equal to .

Solution to Frame 4-24.

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In the U.S. system, a gallon equals four quarts. A quart is a little smaller than a liter. About how much is a gallon of gasoline when measured in the metric system?

Solution to Frame 4-25.

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An inch equals 2.54 centimeters (cm).

There are cubic centimeters in a cubic inch.

There are 1000 cubic centimeters in a liter.

How many cubic inches are in one liter?

Solution to Frame 4-26.

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Sand, gravel, concrete, and similar commodities are often sold by the cubic yard. If you purchased a cubic yard of sand, you would be getting about cubic meters of sand.

NOTE: A yard is about 0.91 meters.

Solution to Frame 4-27.

16.4 cc (rounded)

(2.54 x 2.54 x 2.54 =

16.387064)

about 61

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Fill in the blanks on the following chart.

Milliliters Liters Cubic meters

43 mL = =

= 12 L =

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The following shows a conversion chart for U.S. and metric volume measures.

Cubic inches Cubic feet Cubic yards Metric measure

1 0.0006 0.00002 16.4 cc (or mL)

1,728 1 0.037 28.3 L

0.061 1 cc

61 0.035 1 L

100 cubic inches equals about (metric measure).

12,000 mL = 12 L =

3,000,000 mL =

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The following shows a conversion chart using U.S. liquid volume measures. Cubic inches is included to provide for conversion from U.S. customary liquid measures to U.S. customary measures.

Fluid

Ounce Pint Quart Gallon Cubic inch Metric

1 0.0625 0.03125 0.0078125 1.80 30 mL

16 1 0.5 0.125 28.88 0.47 L

32 2 1 0.25 57.75 0.95 L

128 8 4 1 231 3.79 L

Solution to Frame 4-30.

1.64 L

16.4 mL x 100 =

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UNITS OF MASS (WEIGHT). Four major metric units of mass are:

milligram (mg) -- 1/1,000 gram

gram (g)

kilogram (kg) -- 1,000 grams

metric ton -- 1,000 kg or 1 megagram

The milligram is so light (about the weight of a grain of sugar) that it is seldom used except in medicine and other scientific areas. The megagram or metric ton (about 2205 pounds) is used for heavy things. The metric ton is about 10 percent heavier than the U.S. short ton (2,000 pounds), but a little lighter than the U.S. long ton (2,240 pounds).

a. An object weight 350 milligrams. It weighs _________ grams.

b. An object weight 1285 grams. It weighs ________ kilograms.

c. An object weighs a quarter of a kilogram. How many grams does it

weigh?

d. How many grams are in a metric ton?

e. How many pounds (to the nearest 100 pounds) are in a metric

ton ?

f. How many U.S. short tons are in an U.S. long ton? _____________

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The following chart shows conversions using U.S. weights. The weights are the avoirdupois system, which is the common weighing system for commerce. There are other systems of weights such as the apothecaries' (for pharmacy) and troy (used for precious metals such as gold). The avoirdupois, apothecaries' weight, and troy weight systems are based upon the grain, which is the same in all three systems. In the avoirdupois system, a pound equals 7,000 grains and is divided into 16 ounces. In the apothecaries' and troy systems, a pound equals 5,760 grains and is divided into 12 ounces.

Grain Ounce Pound Metric

1 0.0023 0.00014 64.8 mg

437.5 1 0.0625 28.35 g

7,000 16 1 454 g (0.454 kg)

1 grain = 64.8 milligrams

20 grains = 1 scruple (1.3 grams)

3 scruples = 1 dram (3.9 grams)

8 drams = 1 ounce (31.1 grams)

12 ounces = 1 pound (373 grams)

1 grain = 64.8 mg

480 grains = 1 ounce (31.1 grams)

12 ounces = 1 pound (373 grams)

a. Which is heavier, an ounce of iron (avoirdupois weight) or a ounce

of gold (troy weight)?

b. Which is heavier, a pound of iron (avoirdupois weight) or a pound

of gold (troy weight)?

NOTE: The U.S. weights used in Frame 4-32 are the common avoirdupois weights.

Solution to Frame 4-32.

a. 0.35

b. 1.285

c. 250

d. 1,000,000

e. 2200

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The following shows a conversion chart for changing from the U.S. Customary System of weights to metric units (values are approximate).

1 grain = 64.8 milligrams

1 ounce = 28.4 grams

1 pound = 454 grams or 0.454 kilograms

1 hundredweight = 100 pounds = 45.4 kilograms

1 ton = 20 hundredweight = 907 kilograms = 0.907 metric tons

Convert the following U.S. weights to metric units (round to nearest tenth).

a. 3 pounds = about ____________ grams

b. 7 pounds = about ____________ kilograms

c. 3 ounces = about ____________ grams

d. 7.5 tons (short) = about ____________ metric tons

a. gold

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The following shows a conversion chart for changing from the metric system to U.S. Customary System (values are approximate).

1 milligram = 0.000035 ounces = 0.015 grains

1 gram = 0.035 ounces = 15 grains

1 hectogram = 100 grams = 3.5 ounces = 0.22 pounds

1 kilogram = 2.2 pounds

1 metric ton = 2205 pounds = 1.1 short tons

Convert the following metric measurements to U.S. Customary Standard units of weight.

a. 2.5 metric tons = ____________ tons (short)

b. 650 grams = ___________ ounces

c. 4 kilograms = __________ pounds

d. 1 kilogram = ______________ ounces

Solution to Frame 4-34.

a. 1362 g

b. 3.2 kg (3.178)

c. 85.2 g

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UNITS OF AREA. Metric units for measuring area include the square centimeter (1 cm by 1 cm), the square meter (1 meter by 1 meter), the are (10 meters by 10 meters), the hectare (100 meters by 100 meters), and the square kilometer (1000 meters by 1000 meters).

1 square meter = 10,000 square centimeters = 1 centare (0.01 are)

1 are = 100 square meters

1 hectare = 100 are = 10,000 square meters

1 square kilometer = 100 hectare = 10,000 are = 1,000,000 sq. meters

An area of 12 square kilometers contains hectares

a. 2.75 tons

b. 22.75 ounces

c. 8.8 pounds

d. 35.2 ounces

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In the U.S. Customary System, area is measured using the square inch, square foot, square yard, acre, or square mile.

1 square foot = 144 square inches

1 square yard = 9 square feet = 1296 square inches

1 acre = 4,840 square yards = 43,560 square feet

1 square mile = 640 acres

An area of land measuring 70 yards by 70 yards is equal to a little more than one .

Solution to Frame 4-36

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Information for converting from U.S. Customary System units to metric units is given below. Equivalents are approximate.

1 square inch = 6.5 square centimeters

1 square foot = 0.093 square meters

1 square yard = 0.836 square meters

1 acre = 4, 047 square meters = 40.5 ares = 0.4 hectare

1 square mile = 2.59 square kilometers = 259 hectare

A piece of land one furlong (1/8 mile) square contains _______ acres or about hectares.

Solution to Frame 4-37

acre

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Information for converting from the metric system to the U.S. Customary System units of area is given below. Equivalents are approximate.

1 square centimeter = 0.155 square inches

1 square meter = 10.8 square feet = 1.2 square yards

1 are = 0.025 acres = 120 square yards

1 hectare = 2.48 acres

1 square kilometers = 0.386 square miles

A piece of land one kilometer by one kilometer contains about acres.

Solution to Frame 4-38

10 acres

(1/8 x 1/8 = 1/64

640 x 1/64 = 10)

4 hectare

(259/64 = 4.04688

or

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Two primary points to remember when working with the Celsius scale are:

Solution to Frame 4-39

247 acres

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Five degrees on the Celsius scale is equal to ______ degrees on the Fahrenheit scale.

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A quick comparison of the Celsius and Fahrenheit scales is shown below.

If you have average body temperature, your oral temperature is

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Remember: When converting from Celsius to Fahrenheit or from Fahrenheit to Celsius, you must adjust for the different freezing temperatures.

The formula for converting from Celsius to Fahrenheit is

When converting from Celsius to Fahrenheit, you multiply by ,

then add to the product.

Solution to Frame 4-42

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Remember, when converting from Celsius to Fahrenheit, you multiply first, then add.

Convert the following Celsius temperatures to Fahrenheit using either of the formulas given in Frame 4-41. The formulas are the same except one uses a decimal form (1.8) and the other uses a fraction form (9/5).

9/5 (or 1.8)

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Remember, when converting from Fahrenheit to Celsius, you

first, then multiply (or multiple and divide).

a. 32 [0 x 9/5 = 0;

0+32 = 32]

b. 212 [100 x 9/5 =

180; 180 +

32 = 212]

c. 100.4 [38 x 1.8=

68.4; 68.4+

32 =100.4]

d. 413.6 [212 x 1.8 =

381.6;

381.6 + 32=

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Convert the following Fahrenheit temperatures to Celsius using either of the formulas given in Frame 4-43.

Solution to Frame 4-45

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The answer to both of the above questions must be, "No," because we know of temperatures that go below 0 on each scale. But scientists desired a system of measurement in which the temperature measured the heat energy of an object, beginning with no heat energy. They gave the term "absolute zero" to this temperature. In 1848, William Thomson (later Baron Kelvin of Largs) introduced the absolute temperature scale based upon the Celsius scale. In this thermodynamic scale of temperature, an object with a temperature of zero has no heat energy. This temperature is referred to a zero kelvin (0 K). The freezing point of water is 273.15 K and the boiling point of water is 373.15 K. In 1954, the kelvin scale was adopted as the SI standard.

The temperature at which an object contains no heat energy is .

a. 0 [32 – 32 = 0

0 x 5/9 = 0;

b. 37.8. [100 – 32 =

68; 68 x

0.5556 = 37.7808]

c. 100 [212–32 =180

180 x 5/9 =

100]

d. –17.8 [0 – 32 =

–32;

–32 x 5/9 =

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a. The temperature at which pure water freezes is K.

b. The temperature at which pure water boils is K.

c. Of the Fahrenheit, Celsius, and kelvin scales, which has/have no

negative temperatures?

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If you feel that you need more review, look over the appropriate frames again. Then work the following self-test exercises shown below and on the following page. The solutions are found on the page following the self-test.

a. 273.15

b. 373.15