1.2 units of measurement
from handson chemistry
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1.2.1 THE IMPORTANCE OF UNITS 4
1.2.2 UNITS IN CHEMISTRY 7
1.2.3 Problem Solving (Dimensional Analysis) 12
FOR THE TEACHER 17
1.2.1 THE IMPORTANCE OF UNITS 18
1.2.2 UNITS IN CHEMISTRY 19
1.2.3 Problem Solving (Dimensional Analysis) 22
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 boardfoot, 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 19:3536). 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 submultiples:
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

10^{18}

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

exa

E

10^{15}

1,000,000,000,000,000

peta

P

10^{12}

1,000,000,000,000

tera

T

10^{9}

1,000,000,000

giga

G

10^{6}

1,000,000

mega

M

10^{3}

1,000

kilo

k

10^{2}

100

hecto

h

10^{1}

10

deka

da

10^{0}

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

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