# Decimal fraction

A decimal fraction or decimal fraction is a fraction whose denominator is a power of ten with natürlichzahligem is exponent - or, in simpler terms, a fraction, in which the denominator is 10 ( ) 100 ( ), 1000 ( is) and so on. ${\ displaystyle 10 ^ {1}}$${\ displaystyle 10 ^ {2}}$${\ displaystyle 10 ^ {3}}$

The decimal fraction can be written directly as a decimal number in the tens system . Here, the fractional parts are separated from the integer part with a decimal separator . All fractions whose abbreviated forms have no prime divisors other than two and five in the denominator can be represented as a decimal fraction.

## Examples

An example:

${\ displaystyle {\ frac {35} {100}} = 0 {,} 35 = 10 ^ {- 1} \ cdot 3 + 10 ^ {- 2} \ cdot 5}$

More generally, non-terminating (infinite or periodic ) decimal numbers (such as, for example ), which obviously cannot be written as a fraction with a power of ten in the denominator, or irrational numbers (such as the circle number Pi or Euler's number e ) can be called decimal fractions become. A decimal fraction expansion is also used here. ${\ displaystyle 0 {,} 11111 ...}$

## history

Archaeological finds suggest that decimal fractions for units of measure were used as early as 2800 BC. Were used in India. The oldest known text on the use of decimal fractions comes from Al-Uqlidisi from around 952.

The current spelling with the separation by comma or point was used by Bartholomäus Pitiscus in his trigonometric tables in 1612 and then by John Napier in his articles on logarithms in 1614 and 1619. However, it was used before ( Francesco Pellos , Christoph Clavius ).

## Pronunciation of decimal places of a decimal fraction

Places after the decimal point are shown by listing the individual digits: "Pi is three decimal point one four one five nine two ...". If you want to include the evaluation of the digit, then you can again break down into individual fractions , usually like the digits in front of the comma in groups of three according to the technical notation from the SI system in decimal fractions: "Pi is three, one hundred and forty-one thousandths, five hundred and ninety-two millionths, ... ". The phrase “Pi is three point fourteen fifteen ...” is incorrect.

### Currencies

For currencies that have special sub-units, such as For example, with the euro the cent as a hundredth, the specification in whole main units and whole sub-units, "three euros, fourteen cents", is common, although the name of the sub-unit is usually not pronounced: "three euros fourteen", the value of the number according to the currency as hundredths is generally clear here. For amounts with higher accuracy, such as fuel prices per liter and telephone tariffs per minute, the formulation as a decimal number, “one point two one nine euros per liter”, or a mixed formulation as “one euro twenty-one-nine” is common.

## literature

• Helmut Pruscha, Daniel Rost: Mathematics for natural scientists . Methods, applications, program codes. 1st edition. Springer, 2008, ISBN 978-3-540-79736-4 , ISSN  0937-7433 , p. 3 ff .