Decimal Fractions
All common fractions can be converted to decimal fractions by dividing the numerator by the denominator. For example:
Ancient mathematical records—Hindu-Arabic, Greek, Egyptian, and Babylonian—show many different methods for noting fractions. However, Islamic scholars were the first to convert fractions to decimal analogues. During the Middle Ages, scholars used the Babylonian system of sexagesimal (base 60) fractions for computation, particularly when calculating square roots and cube roots. In the fifteenth century, the astronomer al-Kashi invented a method for converting sexagesimal fractions to decimal fractions. Al-Kashi also discovered a way to approximate the value of 2 in both sexagesimal and decimal fractions.
Despite al-Kashi's discovery, the use of decimal fractions evolved very slowly. Johannes Regiomontanus (1436-1476) compiled tables of sines and cotangents that were very close to decimal fractions. In 1585, Simon Stevin (1548-1620) was the first to offer conceptual details of decimal fractions and appreciate their significance. Stevin's system was cumbersome because he used a number in a circle to indicate each decimal place: 0 for the units place, 1 for the tens place, and so forth. The 1616 English translation of the logarithms of John Napier (1550-1617) marked the first time the decimal point appeared in print. In the late seventeenth century, some mathematicians were signifying a decimal by using the left half of a pair of brackets or other such notations. Decimal fractions still not used universally until the eighteenth century; until then, about half of the arithmetic texts mentioned decimals and half did not.
The International System of Units (SI) favors the use of the decimal comma as a decimal marker and most countries follow this form. Many countries used a decimal comma even before the SI recommendation. Most English-speaking countries use a decimal point. In the British press, sometimes a dot raised halfway above the line is used as a decimal marker. This notation causes difficulty because it can be mistaken for a multiplication sign. Many English-speaking countries have started calling the entire number a decimal rather than a decimal fraction. Strictly speaking, a decimal is the part that follows the decimal marker. When reading a decimal fraction out loud, "point" is a common abbreviation for "decimal point." For clarity, decimal fractions whose absolute value is less than one are written with the unit zero in front of the decimal point--for example, 0.5.
In long decimal fractions, digits are often divided into groups of three, working both ways from the decimal marker:
In scientific tables, by contrast, the digits are often shown in groups of five.
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