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3-2 Everything Decimals CH 3]

Your hand held calculator requires that arithmetic operations with fractions be
performed in decimal form only, thus fractions in computations must be converted to
decimal form. For example, to compute the cost of 576 ½ pounds of seed at $15.50 per
pound, the fraction ½ is changed to 0.5, which is an equivalent decimal fraction. The
computation then becomes 576.5 times $15.50.

Example A: What is the cost of 576½ pounds of seed at $15.50 per pound?

Solution: 576.5 x $15.50 = 8,935.75 Cost = $8935.75

Obviously the calculation in Example A is facilitated through the use of a decimal
fraction (576.5).

Let’s discuss the parts of each number in this calculation:

The first number in this problem is 576 ½ expressed as a whole number (576) and a fraction (½).
Stated as a decimal number it is 576.5 with 576 being the whole number, the decimal point
followed by the fractional part of the decimal number (5) to the right of the decimal.

The second number in the problem is $15.50, which is written as a decimal number. The $ symbol
tells us that the amount is in dollars. The whole number is 15 with a decimal point and the decimal
fraction, to the right of the decimal point is 50.
Aliquot: Contained
an exact number of It is necessary that you be adept at using both decimal fractions and aliquot parts. You
times in something should also be able to mentally convert commonly-used fractions from one form to the other,
else — used of a and of course a hand held calculator will facilitate the conversion to a decimal equivalent
divisor or as a part. and in your calculations.
Example: 5 is an
aliquot part of 15.
NUMBER

WHOLE NUMBER DECIMAL POINT

$ 8 9 3 5 . 7 5

DECIMAL FRACTION
Figure 3.1

THE IDEA OF THE DECIMAL FRACTION, A BEGINNING
The idea and concept for the decimal notation is credited to Simon Stevin 1548–1620),
sometimes called Stevinus, a Flemish mathematician, physicist and military engineer, and
John Napier (1550—1627) of Scotland, a mathematician and theological writer who
originated the concept of logarithms as a mathematical device to aid in calculations. Simon
Stevin published the first book on decimals, La Disme, in 1585 whereby he acknowledged
and documented the importance of decimal fractions. Stevin explained the theory of
operations with decimals and began the formal notation of the decimal; The English, at the
time, used 3·14, the French used 3,14 and we today use 3.14 to state a decimal value.
Stevin emphasized the utility of decimal arithmetic “for all accounts that are encountered in
the affairs of men,” and he explained in an appendix how it could be applied to surveying,
stereometry (the measurement of solid bodies – geometry), astronomy, and measurements
(mensuration). His idea was to extend the base-10 positional principle to numbers with
fractional parts, with a corresponding extension of notation to cover these cases. In his
system the number 237.578 was denoted in which the digits to the left of the decimal point
are the integral part of the number. To the right of the decimal point are the digits of the
fractional part, with the first decimal point value equal to 1/10 of 1 which is 0.1; and the
next value is 1/10 of 1/10 which is 1/100 of one, written as 0.01; and each successive
value decreased in the same method. Stevin showed how the usual arithmetic of whole

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