 |
|
|
The evolution of notation for decimals |
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 gradually 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.
The evolution of notation for decimals
Modern methods of writing decimals were invented less than 500 years ago. However, the use of decimals in various forms can be traced back thousands of years. The Babylonians used a number system based on 60 and extended it to deal with numbers less than 1. Some use of decimals was also made in ancient China, medieval Arabia and in Renaissance Europe.
In his book Canon-mathematicus (1579) the Italian/French mathematician Francois Viete called for the use of base ten decimals rather than base 60 sexagesimal "decimals" 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." |
It was a book by Simon Stevin from Netherlands, published in 1585, entitled De Thiende (The Tenth) which familiarised more people with decimals. He sought to teach everyone "how to perform with an ease unheard of, all computations necessary between men by integers without fractions". The notation however, was different to today's. This is illustrated in the table below with the approximate value of pi.
|
Modern notation for pi |
3.1416 |
|
Stevin wrote |
3 (0) 1 (1) 4(2) 1(3) 6(4) |
|
or |
|
|
This notation shows the number is |
|
|
which is the same as |
|
Many other variations of decimal notation have existed in the past as shown in the following table adapted from Tobias Dantzig's (1954) book, "Number: the Language of Science".
Decimals 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 and others like South Africa still use the decimal comma.
All of the schemes above are different ways of marking where the ones column is. This is the central purpose of the decimal point. Explain it this way to students.
|
OUR MOTTO: |