1.2 UNITS OF MEASUREMENT

1.2.1 Units of Measurement

1.2 units of measurement

from hands-on chemistry

Copyright Prentice-Hall

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http://www.csun.edu/~vceed002/Herr/HANDS_ON_SCIENCE.htm

31.2.1 THE IMPORTANCE OF UNITS

1.2.2 UNITS IN CHEMSITRY6

1.2.3 PROBLEM SOLVING (dimensional analysis)11

FOR THE TEACHER15

1.2.1 THE IMPORTANCE OF UNITS16

1.2.2 UNITS IN CHEMISTRY17

1.2.3 PROBLEM SOLVING (Dimensional Analysis)19

An accurate and consistent system of measurement is the foundation of a healthy economy. In the United States, a carpenter pays for lumber by the board-foot, while a motorist buys gasoline by the gallon, and a jeweler sells gold by the ounce. Land is sold by the acre, fruits and vegetables are sold by the pound, and electric cable is sold by the yard. Without a consistent, honest system of measurement, world trade would be thrown into chaos. Throughout history, buyers and sellers have tried to defraud each other by inaccurately representing the quantity of the product exchanged. In the Bible we read that the people of Israel were commanded to not "...use dishonest standards when measuring length, weight or quantity" but rather "use honest scales and honest weights..." (Leviticus 19:35-36). From ancient times to the present there has been a need for measuring things accurately.

When the ancient Egyptians built monuments like the pyramids, they measured the stones they cut using body dimensions every worker could relate to. Small distances were measured in "digits" (the width of a finger) and longer distances in "cubits" (the length from the tip of the elbow to the tip of the middle finger; 1 cubit = 28 digits). The Romans were famous road builders and measured distances in "paces" (1 pace = two steps). Archaeologists have uncovered ancient Roman roads and found "mile"-stones marking each 1000 paces (mil is Latin for 1000). The Danes were a seafaring people and particularly interested in knowing the depth of water in shipping channels. They measured soundings in "fathoms" (the distance from the tip of the middle finger on one hand to the tip of the middle finger on the other) so navigators could easily visualize how much clearance their boats would have. In England distances were defined with reference to body features of the king. A "yard" was the circumference of his waist, an "inch" was the width of his thumb, and a "foot" the length of his foot. English farmers, however, estimated lengths in something they could more easily relate to: "furlongs", the length of an average plowed furrow.

As various cultures emigrated to England, they brought with them their various measurement systems. Today, the English or Customary system reflects the variety of different measurement systems from which it originated. There are, for example, many units in which distance can be measured in the Customary system, but they bear no logical relationship to each other:

1 statute mile = 0.8688 nautical miles = 1,760 yards = 320 rods = 8 furlongs =5280 feet = 63360 inches = 880 fathoms = 15840 hands

Many English units are specific to certain professions or trades. A sea captain reports distances in nautical miles and depths in fathoms, while a horse trainer measures height in hands and distance in furlongs. Unfortunately, most people have no idea what nautical miles, fathoms, hands, or furlongs are because they only use the more common measures of miles, yards, inches.

The early English settlers brought the Customary system of measurement with them to the American colonies. Although the Customary system is still widely used in America, scientists prefer to use the metric system. Unlike the English (Customary) system, the metric system did not evolve from a variety of ancient measurement systems, but was a logical, simplified system developed in Europe during the seventeenth and eighteenth centuries. The metric system is now the mandatory system of measurement in every country of the world except the United States, Liberia and Burma (Myanmar).

In 1960, an international conference was called to standardize the metric system. The international System of Units (SI) was established in which all units of measurement are based upon seven base units: meter (distance), kilogram (mass), second (time), ampere (electrical current), Kelvin (temperature), mole (quantity), and candela (luminous intensity). The metric system simplifies measurement by using a single base unit for each quantity and by establishing decimal relationships among the various units of that same quantity. For example, the meter is the base unit of length and other necessary units are simple multiples or sub-multiples:

1 meter = 0.001 kilometer = 1,000 millimeters =1,000,000 micrometers = 1,000,000,000 nanometers

Table 1 shows the SI prefixes and symbols. Throughout this book we use the metric system of measurement.

Table 1: SI Prefixes and Symbols

Factor

Decimal Representation

Prefix

Symbol

1018

1,000,000,000,000,000,000

exa

E

1015

1,000,000,000,000,000

peta

P

1012

1,000,000,000,000

tera

T

109

1,000,000,000

giga

G

106

1,000,000

mega

M

103

1,000

kilo

k

102

100

hecto

h

101

10

deka

da

100

1

10-1

0.1

deci

d

10-2

0.01

centi

c

10-3

0.001

milli

m

10-6

0.000 001

micro

m

10-9

0.000 000 001

nano

n

10-12

0.000 000 000 001

pico

p

10-15

0.000 000 000 000 001

femto

f

10-18

0.000 000 000 000 000 001

atto

a

1.2.1 THE IMPORTANCE OF UNITS

Concepts to Investigate: Fundamental units, derived units, factor labels, dimensions.

Materials: none.

Principles and Procedures: When crossing the border to Canada, American motorists are often surprised to see speed limits of "90" or "100". If they don't realize that Canadians measure speed in kilometers/hr while Americans measure in miles/hr (1.00 mile/hr = 1.61 kilometers/hr; 60 miles/hr = 97 km/hr) they may soon be in for trouble with the law. If, for example, an American motorist accelerates until her speedometer (measured in miles/hr) reaches "100", she will be traveling 38 miles/hr over the posted speed limit of 100 km/hr since a speed of 100 km/hr is equal to only 62 miles/hr. As this example illustrates, measurements without units are meaningless and may lead to serious misunderstandings. Everything that can be measured must be expressed with appropriate units.

Units in everyday life: We use units everyday, often without even realizing it. In the statements that follow you will find a wide variety of interesting facts, but each is missing a crucial piece of information -- the dimensions (units)! All the statements are meaningless until you supply the appropriate units. On the basis of your experiences, try to match the appropriate units from the list provided.

carats

cm

degrees Celsius

degrees Fahrenheit

feet

grams/ml

inches

kcal (Cal)

kilograms

kilometers

kilowatt-hours

liters

megabars

miles

miles per hour

milligrams

pounds

stories

tons

yards

(a) America's tallest building (Sears Tower in Chicago) is 110 ___ high.

(b) The Empire State Building in New York is 1250 ___ high.

(c) The Nile is the world's longest river. It is 4180 ___ long.

(d) The Amazon River in South America is ___ 6296 long.

(e) The coldest temperature ever recorded was -128.6 ____ in Vostok, Antarctica in 1983.

(f) The highest recorded temperature in the United States was in Death Valley, California when the mercury reached 57 ____!

(g) The world record rainfall occurred in Cherrapunji, India where 1042 ___ of rain fell in one year.

(h) The largest recorded hailstone to ever fall landed in Coffeyville, Kansas in 1979. It had a diameter of 44.5 _____ !

(i) The longest punt in NFL history was by Steve O'Neal of the new York Jets. He kicked the football 98____.

(j) The largest seed in the world is that of the coc-de-mer coconut tree, which may weigh as much as 40 ____!

(k) The world's largest meteorite is located in Southwest Africa. It weighs 650 ________ .

(l) The most popular soft drink in the World is currently Coca Cola(. More than 210 million ______ were consumed each day in 1990.

(m)The largest diamond in the world was mined from South Africa in 1905 and weighs 3,106 _______ .

(n) Earth is the densest of the nine planets, with an average density of 5.515 _____ .

(o) The world's fastest aircraft is the Lockheed SR-71 Blackbird, clocking a record speed of 2,193.67____.

(p)The largest gold nugget ever found had a mass of 100 ________ !

(q) One large chicken egg contains an average of 274____ cholesterol.

(r) A 16-year old male requires an average of 2800 ____ of energy per day while a an average 16-year old female requires only 2100____.

(s) The United States produces and consumes more electric energy than any other nation. Each year the United States produces over 2500 billion ____ .

(t) The largest pressure ever developed in a laboratory was 1.70 ______, used to solidify hydrogen in 1978.

Questions: