The Handy Math Answer Book

(Brent) #1

But like most measurements over time, not all gallons were alike. During the
American colonial period, the gallons from British commerce were based on dry and
liquid commodities. For dry, the gallon was one-eighth of a Winchester bushel
(defined by the English Parliament in 1696 as a cylindrical container 18.5 inches in
diameter by 8 inches deep), which held 268.8 cubic inches of material. It was also
called a “corn gallon” in England. For liquid, in England the gallon measurement was
based on Queen Anne’s wine gallon (also called the traditional British wine gallon),
which measured exactly 231 cubic inches. This is why volume measurements in the
United States include both the dry and liquid units, the dry units being about one-
sixth larger than the corresponding liquid units.


By 1824, the British weren’t as satisfied with the gallon divisions as the Ameri-
cans. In response, the British Parliament abolished all the traditional gallons and
established a system based on the Imperial gallon. It is still in use today, measuring
277.42 cubic inches, with the container holding exactly 10 pounds of water under spe-
cific (such as temperature and pressure) conditions.


What is a rate?


The rate is often used in measurement. It is defined as the comparison by division
(similar to a ratio). For example, when measuring miles or kilometers per hour in
your car, the rate equates the pairs of miles (kilometers) with hours. The translation
for “a rate of 65 miles per hour” is that for each hour one will travel 65 miles as long
as the speed remains the same for that hour.


What is accuracy in measurement?


Accuracy in measurement is based on relative errorand number of significant digits.
Relative error is the absolute error divided by the calculated (or estimated) value. For
example, if a person expects to spend $10 per week at the local espresso bar, but he or
she actually spends $12.50, the absolute error is 12.50 10.00 2.50; the relative
error then becomes (2.50/10) 0.25 (to find out the percent, multiply by 100, or 0.25
 100 25 percent of the original estimate).


Significant digits refers to a certain decimal place that determines the amount of
rounding off to take place in the measurement. In most cases, this means that there
are more numbers to the right of the decimal point. But beware. Accuracy in measure-
ment does not mean the actual measurement taken was accurate. It only means that if
there are a large number of significant digits, or if the relative error is low, the mea-
surement is more accurate.


What are some common modern measurement systems?


There are several measurement systems in use today. The English customary system
is also known as the standard system, U.S. customary system (or units), or English 49


MATHEMATICS THROUGHOUT HISTORY

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