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CH 3] Calculating Business 3-3

numbers could be extended to decimal fractions, using rules that determined the
positioning of the negative powers of 10 (i.e. a tenth, a hundredth, a thousandth and so
forth).
In 1603 La Disme was translated into English, and in 1617 John Napier used decimal
fractions in his Rabdologiae, seu Numerationis per Virgulas Libri Duo (Study of Divining Rods, or
Two Books of Numbering by Means of Rods, 1617) The “Divining Rods” referenced here is the initial
development of the slide rule, which were used in our modern times to put Neil Armstrong, the first
man, on the moon. In 1617 Napier’s treatise on the discovery of logarithms describing three
devices to aid arithmetic calculations. The devices themselves don't use logarithms, rather
they are tools to reduce multiplication and division of natural numbers to simple addition and
subtraction operations. In his treatise Napier suggested the use of the dot or the comma as a
separator in the decimal and today we use the dot. Because of Napier’s vacillation between

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Figure 3.2 John Napier’s “Divining Rods”: the modern slide rule.

the dot and the comma we find that in France, Germany, Italy, and the Scandinavian
countries, the comma is used for this purpose; while in England the dot is placed above the
line of writing, midway between the top and bottom of the number, i.e. 5·7.
Think on this: these people, from Stevin and Napier, right up to the engineers that
developed our space rockets and engineered aircraft, sending astronauts to the moon,
achieved these accomplishments without the digital computers you are familiar with today;
and their work is the foundation on which our computers digitally function. These men
developed the concepts of the decimal fractions making them more meaningful than fractions.
Decimal fractions are easier to use in arithmetic computations and facilitate the user in
arriving at a concise answer.
Presume that the cost of manufacturing 52,500 bolts is $1,233.75. The cost of each bolt
may be expressed as $1,233.75 / 52,500 . But this is too awkward for many computations.
After this fraction is converted to a decimal fraction by dividing the numerator by the
denominator, the cost per bolt is found to be $0.0235 and the cost per 1,000 bolts is (1000 x
$0.0235=) $23.50. In a similar manner, the accounting department could determine how
much of the $1,233.75 total production cost had been spent for material, labor, and overhead
and then find the per-unit or per-thousand cost of each of these.
These computational results are of value to management in reaching decisions regarding
manufacturing standards, departmental efficiency, controlling expenditures, and establishing
prices. Calculations such as these are made in business, finance or industrially and must be
performed accurately for good results. Accurate computations can only be performed when
one thoroughly understands the meaning and use of decimal fractions.
The decimal numbering is a place-value system of notation employing 10 as the base
requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. In a whole number, the
first place has a value equal to 1, and each place to the left has a value ten times that of the
place to its right. Therefore, each place to the right has a value which is 1/10 of that to its left
(Refer to Figure 3.3 Decimal Value).
The places to the right of the ones position follow the same rule. The first place to the right
of the decimal point has a value equal to 1/10 of 1; the second place, 1/10 of 1/10 , which is
1/100 or 0.01. Refer to Figure 3.3 Decimal Value.

DECIMAL FRACTIONS
A decimal fraction is a number to the right of the decimal point. In a pure decimal fraction

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