Fractional numbers

With the emergence of representations of integers, there were representations of parts of the whole subject. With the advent of natural number n, there was the concept of fractional numbers of the form 1/n. Historically fractional numbers occurred during the measurement. Fractions naturally arises in the solution of problems on the division of property, land measuring, calculating time.

Fractional numbers are found in the most ancient extant written sources  the babylonian clay tablets and egyptian papyri

Fractional numbers are found in the most ancient extant written sources the babylonian clay tablets and egyptian papyri. Sexagesimal fractions are used to this day in the division of angular and arc degrees (hours) for 60 minutes, and minutes into 60 seconds. In ancient Rome was an interesting system of fractional numbers. It was based on the division of the Roman unit of mass asse. Asse divided into 12 equal parts. Twelfth of the asse named ounce. There were a total of 18 different fractions.

Fractional numbers recorded by the numerator and denominator appeared in ancient Greece. The greeks recorded the top denominator and the numerator below. The very terms "numerator" and "denominator" in the late 12th century the first recorded Maximus Planudes (1260-1310), a greek monk and mathematician. Fractional numbers in the usual form for the first time began to write the Indians about 1500 years ago, but they did not use the line between the numerator and denominator. The line became common only in the 16th century. Simple fraction a ratio of two integers. For the first time the division sign ":" for fractional numbers was used by englishman Johnson in 1633.

Over time, the practice of measurements and calculations showed that it is easier and more convenient to use such measures, in which the ratio of the length of the next two units would be permanent and would be equal to exactly ten base numbering. However, it should be noted that the europeans were not the first who came to the need to use decimal fractional numbers in mathematics. Origin and development of fractional decimal numbers in some Asian countries has been closely linked to the metrology. Already in the 2nd century BC there existed a decimal system of measures of length. Around the 3rd century AD, the decimal system is extended to measures of weight and volume. A more complete and systematic explanation receive decimal fractional numbers in the works of the Central Asian scholar al-Kashi in the 15th century. In his work "Key arithmetic" al-Kashi wrote fractional numbers on a single line using the numbers in the decimal system. He wrote the rules of action with them. The scientist used a number of ways of writing fractional numbers: it applied the vertical bar, the ink is black and red. These decimals he used to improve the accuracy of root extraction. In the 80 years of the 16th century, decimal fractional numbers were "discovered" again in Europe, the dutch mathematician Stevin (15481620). Stevin has not enjoyed a comma, but wrote fractional characters in one line with the figures of an integer.

Since the beginning of the 17th century decimal fractional numbers are beginning to penetrate intensely into the science and practice. In England, as a sign that separates the integer part of the fraction, the point was introduced. Comma as the point was proposed in 1617 mathematician John Napier. In 1592 the italian mathematician Giovanni Maggini entered comma. According to others, a comma was introduced by the german scientist Johannes Kepler (15711630), and a decimal point first recorded german mathematician Christopher Clavius (15371612).

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