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Although he was not the first to use decimal fractions (they are found in the work of the tenth-century Islamic mathematician al-Uqlidisi), it was his tract De Thiende (“The tenth”), published in 1585 and translated into English as Disme: The Art of Tenths, or Decimall Arithmetike Teaching (1608), [3] that led to their widespread adoption ...
For example, "five tenths," is typically a measurement or tolerance of five ten-thousandths of an inch, and written as 0.0005 inches. "Three tenths," as another example, is written as 0.0003 inches. [9] Machining "to within a few tenths" is often considered very accurate, and at or near the extreme limit of tolerance capability in most contexts.
A decimal fraction is a fraction whose denominator is an integer power of ten, commonly expressed using decimal notation, in which the denominator is not given explicitly but is implied by the number of digits to the right of a decimal separator. The separator can be a period . , interpunct · , or comma , , depending on locale.
French decimal clock from the time of the French Revolution. The large dial shows the ten hours of the decimal day in Arabic numerals, while the small dial shows the two 12-hour periods of the standard 24-hour day in Roman numerals. Decimal time is the representation of the time of day using units which are decimally related.
A real number can be expressed by a finite number of decimal digits only if it is rational and its fractional part has a denominator whose prime factors are 2 or 5 or both, because these are the prime factors of 10, the base of the decimal system. Thus, for example, one half is 0.5, one fifth is 0.2, one-tenth is 0.1, and one fiftieth is 0.02.
However, it is useful when comparing with other very large quantities, such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. Kasner used it to illustrate the difference between an unimaginably large number and infinity , and in this role it is sometimes used in teaching ...
Thus, the reading for metric micrometers of this type is the number of whole millimeters (if any) and the number of hundredths of a millimeter, as with an ordinary micrometer, and the number of thousandths of a millimeter given by the coinciding vernier line on the sleeve vernier scale.
The Hindu–Arabic system is designed for positional notation in a decimal system. In a more developed form, positional notation also uses a decimal marker (at first a mark over the ones digit but now more commonly a decimal point or a decimal comma which separates the ones place from the tenths place), and also a symbol for "these digits recur ad infinitum".
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