History of Decimals and the Metric System
Contents of this page:
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Decimal money and measurement
The evolution of notation for decimal fractions
Decimal money and measurement
The use of decimals instead of fractions has become much more common and important in
everyday life since the introduction of a decimal system of money and metric measurement.
Australia changed to decimal money (dollars and cents with 100 cents = 1 dollar) in 1966. The
previous system used pounds, shillings and pence (1 pound = 20 shillings, 1 shilling = 12 pence).
Australia changed its system of weights and measures to the metric system during the 1970s. In
the metric system, all conversions between units are based on factors of 10. Time is the only
exception. Otherwise, it is completely compatible with decimal numbers. In the previous
Imperial system, a large number of different conversion factors were used. For example, 16
ounces = 1 pound, 14 pounds = 1 stone, 8 stones = 1 hundredweight, 12 inches = 1 foot, 3 feet =
1 yard, 1760 yards = 1 mile. This made calculations very difficult. The Australian Council of
Educational Research estimated that the change to decimal money and metric measurement freed
up at least 18 months of mathematics lessons in Australian primary schools. (ACER, 1964)
The Imperial system had developed slowly, in an unplanned way. The metric system of
measurement was created and first adopted in France in the 1790s during the revolution, in a
time of great reform. Decimal money was first used in the United States from 1792. France
adopted it in 1799.
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The evolution of notation for decimal fractions
Modern methods of writing decimals were invented less than 500 years ago. Some use of
decimal fractions was made in ancient China, medieval Arabia and in Renaissance Europe. By
about 1500, decimals were well accepted by professional mathematicians but not widely used.
Thousands of years earlier, the Babylonians had used a place-value number system based on 60
(whereas ours is based on 10) and had been extended to deal with numbers less than one. This
was still in use in the 1500s in Europe, but the advantages of a thoroughly base ten system were
becoming apparent. In his book Canon-mathematicus (1579) the Italian/French mathematician
Francois Viete called for the use of base ten decimal fractions rather than base 60 sexagesimal
fractions when he wrote:
"Sexagesimals and sixties are to be used sparingly or never in mathematics, and thousandths and
thousands, hundredths and hundreds, tenths and tens, and similar progressions, ascending and
descending, are to be used frequently or exclusively"
Viete used decimals in this work, but wrote them differently to how we now write them. For
example, for the length of the side of a square inscribed in a circle of diameter of 200 000 he
wrote
which we would write as 141421.35624. (This is a very accurate
approximation to 100 000 times the square root of 2). Later he used
for 100 000
times pi, the number we would write as 314 159.26535. He also used boldface type to indicate
the whole number part of this number, writing it as 314,159,265,36. Sometimes he also included
a vertical stroke to separate the whole number and fractional parts. For example, he wrote
99946.45875 as 99,946|458,75.
The person who is credited with making decimal fractions widely known and understood among
common people and practical users of mathematics in Europe is Simon Stevin of Bruges, in the
Flemish Netherlands. He sought to teach everyone "how to perform with an ease unheard of, all
computations necessary between men by integers without fractions ". In a book entitled De
thiende ("The Tenth") published in 1585, he wrote decimal expressions for fractions by writing
the power of ten assumed as a divisor in a circle above or after each digit.
For example, the approximate value of pi which we write as 3.1416 appeared as
3 (0) 1 (1) 4(2) 1(3) 6(4)
or as
This notation indicated to the reader that the number was
Which is the same as
The use of the decimal point to separate the whole number and fractional parts in decimal
numbers seems to first occur in a 1593 table of values for sines of angles constructed by a friend
of Kepler, either G.A. Magini (1555-1617), a map maker or Christoph Clavius (1537-1612).
Decimal fractions as they look today were used by John Napier, a Scottish mathematician who
developed the use of logarithms for carrying out calculations. The modern decimal point became
the standard in England in 1619. However, many other countries in Europe still use the decimal
comma.
Place value numeration had been in full use for many centuries before its ability to handle
fractions was recognised. Even then, a range of different notations and symbols for separating
the whole number from the fractional part of the number were tried before an accepted method of
writing decimal fractions without the use of unneeded symbols was finally stabilized. The
following table, adapted from Tobias Dantzig's book, Number the Language of Science,
illustrates different ways that decimal fractions were shown prior to the use of our modern
notation.
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