Did You Know: The History of Decimal Point
Did You Know: The History of Decimal Point

The history of Decimal Point(.) seems to be very confusing to us. I found several records from several sources about the beginning of this tiny yet important symbol of Mathematics. This is a fact that has been overlooked by all historians that the credit of being first to use a dot as a separatrix with a full knowledge of its significance belongs to who. I tried to collect some piece of information around internet and found it to be shared here.

As Wikipedia says, A decimal mark is a symbol used to separate the integer part from the fractional part of a number written in decimal form. This is what we all know. We say Mathematics is blessed by Indians. In the Middle Ages, a bar (¯) over the units digit was used to separate the integral part of a number from its fractional part. This practice was derived from the decimal system used in Indian mathematics and was popularized by the Persian mathematicians, when Latin translation of his work on the Indian numerals introduced the decimal positional number system to the Western world. A similar notation remains in common use as an underbar to superscript digits, especially for monetary values without a decimal point, e.g. 9995. Later, a separator (a short, roughly vertical, ink stroke) between the units and tenths position became the norm among Arab mathematicians, e.g. 99ˌ95. When this character was typeset, it was convenient to use the existing comma (99,95) or full stop (99.95) instead.

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. 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”.

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 Christopher Clavius (1537-1612). I found the same name in another article “On the Early History of the Decimal Points” by Jekuthiel Ginsburg: Jesuit father Christopher Clavius, who is often credited for using a dot as a separatrix with a full knowledge of its significance in this connection. In his work on the astrolabe, published in Rome in 1593 he gives a “Tabula Sinuum,” where the proportional parts are separated from the integers by periods (points, dots). A portion of the table is shown below.

Facsimile of "Astrolabe" of Clavius (1593)

Facsimile of “Astrolabe” of Clavius (1593)

So far as now known, this is the first appearance of the decimal point in a work in which its full significance is given. The table antedates the Pitiscus edition of 1608, which has been so carefully studied by Professor Cajori. It also antedates Napier’s Rhabdologia (1617), Wright’s translation of the Mirifici logarithmorum canonis descriptio (1616), and Kepler’s Ausszug auss uralten Messe-Kunst Ar himedis (1616) in each of which the decimal point or comma is used. As to Burgi’s use of symbol in a manuscript of 1592, the claim is no longer seriously considered. The name of Stevin, who wrote the first book upon decimal fractions, need not to be considered in this connection since he made no use of the symbolism under discussion. It remains to consider whether Clavius understood the significance of the symbol, for otherwise he would be entitled to but little more credit than Pellos who, in 1492, wrote 5383694.3 as the quotient of 53836943 by 10, but showed no further appreciation of decimals.

In fact 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

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.

Place value numeration had been in full use for many centuries before its ability to handle fractions was recognized. 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.

Recently, in the 22nd General Conference on Weights and Measures declared in 2003 that “the symbol for the decimal marker shall be either the point on the line or the comma on the line”. It further reaffirmed that “numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups”. This usage has therefore been recommended by technical organizations, such as the United States’ National Institute of Standards and Technology.

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