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Objectives:
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to understand the evolution of measurement systems and how they have changed over the years
to understand the concept of and use of Scientific Notation
to recognize the prefixes associated with the Metric System and understand their interrelatedness
to practice working with the most common examples of the Metric System and common conversions
to learn how to make the interconversions necessary for temperature measurements
to acquaint yourself with some of the most common types of laboratory equipment
to use all of the practice problems as a means of testing yourself in these respective areas
Introduction: "Evolution of Measurement Systems

All cultures have developed measurement systems for communicating and expressing amounts of time. In simple societies, approximations were sufficient and related to familiar objects or body parts. As a result, many early systems used 'human as the measure.' For example, Romans divided the foot into 12 parts called unciae (inches), each of which equaled the breadth of a thumb. Another widely used standard for the inch was the'length of three barleycorns, round and dry' taken from the center of an ear and placed end to end. Similarly, the definition of a mile as 1000 paces (5000 feet = 4/5 meridian mile) later led to the statute mile (5280 feet), and a yard was once defined as the distance from King Henry's nose to the end of his thumb."(Moore, p.213)

"Since there was little exchange between early cultures, numerous systems for measurement evolved. Few of us know that 32 gills equals 1/2 peck equals 1/9 firkin equals 1280 drachms, or that each of these measurements is equivalent to a gallon. Also, the term "mile" had many meanings, depending on the descriptor - an Irish mile equaled 2.05 km, a Scottish mile equaled 1.81 km, an international nautical mile equaled 1.85204 km, a postal mile equaled 1.59 km and a statute (land) mile equaled 1.61 km. The number of prefixes and terms seemed endless, and various standards often led to the same term having different meanings."(Moore, p.213)

"Increased communication among cultures led to standardization of measurement systems. For example, the British imperial system evolved rather haphazardly from Babylonian, Egyptian, Roman, Anglo-Saxon and Norman French systems. This system was loosely adopted by the U.S., and today is called the customary system. Interestingly the U.S. customary and British imperial systems are not identical. For example, one inch in the U.S. equals 2.540005 cm, while an inch in the British imperial system equals 2.539998 cm.

The Beginnings of the Metric System

A Flemish mathematician, Simon Stevin, first published a description of the decimal system. This became the foundation of the metric system. Using a unit of length called the meter was first proposed in 1670 by Gabriel Mouton. It was not until 1790 that the French government imposed the Decimal Metric System based on the meter, liter, and gram. The system so outraged the public that it was rejected in 1793 and not reintroduced until 1837. By 1875, The Treaty of the Meter was signed by representatives of 17 countries and an International Bureau of Weights and Measures was established. This bureau, in 1960, proposed Le Systeme International d'Unites or the International System of Units (known as SI). Since 1960 ALMOST all other countries had gone metric. Only Liberia, Burma, and the United States have not officially converted to SI. Ironically, in the US. the metric system remains the only lawful measurement system and the only system acknowledged legislatively."(Moore, p.214)

SCIENTIFIC NOTATION

Scientists often use numbers that are so large or so small that they dazzle and confuse the mind. For example, the diameter of the nucleus of an atom is about 0.0000000000001 centimeters.

The diameter of the nucleus of an atom is .000 000 000 000 01 meters or 1 x 10_{14}. In very small or very large numbers it is often difficult to keep track of the zeros in such quantities. It is also extremely difficult to express these values in words. Therefore, scientists have found it convenient to express such numbers as powers of 10 and to refer to this form as scientific notation.

Definitions

A POWER or EXPONENT indicates how many times the base number(in this case 10) is multiplied by itself.

10^{0} = 1. By definition, any number raised to the zero power is equal to one (except 0, which is equal to 0).

POSITIVE EXPONENTS represent multiples of 10. For example,10^{2} means 10 x 10 or 100. Positive exponents are used to indicate numbers GREATER than 1.

NEGATIVE EXPONENTS are used to indicate fractions of 10.

10^{-2} means 1/10^{2} = 1/10 x 1/10 which equals 1/100 or 0.01.

Negative exponents are used to indicate numbers LESS than 1.

To get a number into scientific notation form. MOVE THE DECIMAL POINT SO THAT ONLY ONE DIGIT, BETWEEN 1 AND 9 INCLUSIVE, IS TO THE LEFT OF THE DECIMAL POINT. THEN MULTIPLY THIS DIGIT BY 10 RAISED TO AN EXPONENTIAL VALUE CORRESPONDING TO THE NUMBER OF PLACES THE DECIMAL POINT WAS MOVED.

Examples

Convert 7000 to proper scientific notation

7000 = 7 000 = 7.0 x 10^{3}

move the decimal point three spaces to the left

Convert 0.00083

0.0008 3 = 8.3 x 10^{-4}

move the decimal point four spaces to the right

REMEMBER THE MEANING OF POSITIVE AND NEGATIVE EXPONENTS.

COMMON PREFIXES OF THE METRIC SYSTEM

Prefix Symbol Meaning Multiply Unit By: Factor

tera- T trillion 1,000,000,000,000 10^{12}

giga- g billion 1,000,000,000 10^{9}

mega- M million 1,000,000 10^{6}

KILO- k thousand 1,000 10^{3}

hecto- h hundred 100 10^{2}

deca- da ten 10 10^{1}

BASIC UNITS - meters, liters, grams 10^{0}

deci- d tenth 0.1 10^{-1}

CENTI- c hundredth 0.01 10^{-2}

MILLI- m thousandth 0.001 10^{-3}

MICRO- u millionth 0.000 001 10^{-6}

nano- n billionth 0.000 000 001 10^{-9}

pico- p trillionth 0.000 000 000 001 10^{-12}

A centimeter is a hundredth of a meter, a centiliter is a hundredth of a liter, and a centigram is a hundredth of a gram. A kilogram is a thousand grams, a kiloliter is a thousand liters and a kilometer is a thousand meters.

One of the useful features of SI is that the different types of measurements have particular relationships to each other. A liter of water has a mass of a kilogram. A cubic centimeter of water is also a milliliter of water (often drugs that used to be given in "cc's" are now given in "mL's" - same units but different names)

A calorie is the amount of heat it takes to raise one gram of water one degree Celsius. (We Americans don't even get this right- what we call a food calorie is actually equivalent to a kilocalorie!)

Common Metric Units

LENGTH - the METER is slightly longer than a yard = 39.37"

one inch = 2.54 centimeters (cm)

one foot = 30.48 cm

one mile = 1.609 km

one kilometer = 0.6214 miles

VOLUME - the LITER is used to express liquid volume

one liter = 1000 mL

one liter = 1.06 quarts

one quart = 0.946 L

one ounce = 29.56 mL

WEIGHT - the GRAM is the common unit

one pound = 453.6 grams

one kilogram = 2.204 pounds

one gram = 0.035 ounces

Measuring Thermal Energy

The heat content or thermal energy of an object is difficult to measure directly. Consequently, the heat content of one material is usually determined by the change induced in a fluid (usually mercury) within a thermometer. This fluid expands when heated and contracts when cooled at a constant rate over a range of temperatures for which the thermometer is designed. Thermometers used in the laboratory are calibrated in Celsius degrees. Your home thermometer is calibrated in Fahrenheit degrees.

Converting from one system to the other

Since 5 Celsius degrees equals 9 Fahrenheit degrees and since 0 degrees Celsius equals 32 degrees Fahrenheit, the following conversion factors may be used:

9/5 C + 32 = temperature in degrees Fahrenheit

it may also be expressed as 1.8 C + 32 or (9C)/5 + 32

5/9(F-32) = temperature in degrees Celsius

it may also be expressed as 5(F-32)/9

The number 32 is used to adjust for the differences in the zero points of the two scales. BEFORE CONVERTING A FAHRENHEIT TEMPERATURE TO A CELSIUS TEMPERATURE. THE 32 MUST BE SUBTRACTED FROM THE FAHRENHEIT TEMPERATURE to adjust the zero point to correspond to the Celsius scale. This adjustment must be calculated first. When converting a Celsius temperature to a Fahrenheit temperature, the 32 is ADDED TO THE CELSIUS TEMPERATURE AFTER IT HAS BEEN CHANGED TO FAHRENHEIT DEGREES.

A good way to help you check whether you are using the right formula and procedure is to remember that 32 F = 0 C. Therefore, you can plug one or the other into a formula and the answer will tell you if you are using the correct formula.

Go to the following site. Read the materials and take the quiz.

Exercise 1

Express the following numbers, given in scientific notation, to their correct decimal equivalent.

1. 5.01 x 10

2. 3.0 x 10^{-8}

3. 4.555 x 10^{7}

4. 7.2 x 10^{0}

Exercise 2

Express the following numbers in proper scientific notation form.

1. 0.424

2. 0.1111

3. 0.00583

4. 0.00000062

Exercise 3

Carry out the following conversions

1. 25.0 feet to centimeters

2. 3.2 liters to quarts

3. 7 feet, 4 inches to meters

4. 98 pounds to kilograms

5. 2716 grams to pounds

6. 4.00 quarts to liters

7. 1.00 ounces to milligrams

8. 9 yards to millimeters

9. How many inches are there in 35 centimeters?

10. Convert 100 liters to milliliters

11. A gasoline tank has a capacity of 16 gallons. Express this capacity in liters.

12. Suppose your weight is 150 pounds. What is your weight in kilograms?

Although it is possible to convert feet to centimeters directly, this only results in one additional formula for you to learn. It would be better to first convert feet to inches and then use one of the formulas presented earlier.

Exercise

Convert the following temperatures to the opposite scale.

1. 98.6 F

2. 0 C

3. 100 C

4. -17.77 C

5. 100 F

Using Laboratory Equipment

Go to the following site. Acquaint yourself with all of the different types of equipment that could be found in the lab. Answer any questions posed.

Go to the following site. Read the material there. Be aware of the various pieces of equipment that are shown. Answer any questions associated with their use as indicated on the web site.

References Consulted

1. Evans, Richard C. and Edwin A. Wixson. 1977

*A K-12 Handbook of Inexpensive or Easy to Make Metric Measuring Materials with Suggestions for Classroom Use by
Grade Level.*

2. Moore, Randy. "Inching Toward the Metric System," *The American Biology Teacher*, 51(4), April 1989, 213-218.

3. Negus, LeRoy. The Metric System. Ideas for Introducing the Metric System. The University of the State of New York. The State
Education Department. Bureau of General Education Curriculum
Development.