billion
billion | |
---|---|
1000000000 | |
presentation | |
dual | 11 1011 1001 1010 1100 1010 0000 0000 |
Octal | 73 4654 5000 |
Duodecimal | 2 3AA9 3854 |
Hexadecimal | 3B9A CA00 |
Morse code | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - |
Mathematical properties | |
sign | positive |
parity | straight |
Factorization | |
Divider | All figures extending through the term with be represented. (All dividers see running text) |
The word billion (abbreviation: billion , Md. And . Mia ) is the number word for the natural number 1 billion = 10 ^{9} . A billion is equal to a thousand million . The word goes back to the French milliard and, like million, ultimately comes from the Latin mille "thousand". In contrast to the lower case number words like hundred and thousand , billion is a noun and is capitalized. Its use in the sense of a thousand million has only been common in German since the war compensation payments made by France to the German Empire in 1870/1871 .
Math
- 1 billion = 1,000,000,000 = 10 ^{9} ; the billion is therefore a power of ten (number of levels) with the exponent 9.
- 1 billion = 1000 x 1000 x 1000 = 1000 ^{3} ; so the billion is a cube number .
- 1 billion is an even number.
An illustration of the number is provided by the example of a cube with an edge length of one meter, which is divided into small cubes with an edge length of one millimeter - in each of which an average-sized ball at the tip of a ballpoint pen fits. Since one meter is one thousand millimeters, approximately 1000 (width) by 1000 (length) by 1000 (height) of these balls or small cubes fit into the cube, which corresponds to 1 billion (with the balls slipping together due to the ball packing in this simplified example neglected). These one billion stainless steel spheres weigh about 4.2 milligrams per piece at a typical steel density of 8 g / cm³ , which results in a total mass of the one billion spheres of around 4.2 tons , about the weight of three to four average Car. Lined up like a pearl necklace, the beads would make a chain of a billion millimeters or 1000 kilometers, a little longer than the distance from Munich to Rome. If placed close to one another in one plane, the spheres would cover an area of 1000 square meters (e.g. 50 m long and 20 m wide), almost as large as the surface of an Olympic swimming pool (50 m long, 25 m wide).
Divider
Factoring is . This results in so ways a power of two ( up ) with a power of five ( to multiply). The number 1,000,000,000 has exactly the following 100 factors:
- 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1,000, 1,250, 1,280, 1,600, 2,000, 2,500, 2,560, 3,125, 3,200, 4,000, 5,000, 6,250, 6,400, 8,000, 10,000, 12,500, 12,800, 15,625, 16,000, 20,000, 25,000, 31,250, 32,000, 40,000, 50,000, 62,500, 64,000, 78,125, 80,000, 100,000, 125,000, 156,250, 160,000, 200,000, 250,000, 312,500, 320,000, 390,625, 400,000, 500,000, 625,000, 781,250, 800,000, 1,000,000, 1,250,000, 1,562,500, 1,600,000, 1,953,125, 2,000,000, 2,500,000, 3,125,000, 3,906,250, 4,000,000, 5,000,000, 6,250,000, 7,812,500, 8,000,000, 10,000. 000, 12,500,000, 15,625,000, 20,000,000, 25,000,000, 31,250,000, 40,000,000, 50,000,000, 62,500,000, 100,000,000, 125,000,000, 200,000,000, 250,000,000, 500,000,000, 1,000,000,000
Unit of measure prefixes
When referring to units of measurement , billions of times the unit of measurement are referred to with the prefix Giga (abbreviated: G), whereas the billionth part (10 ^{−9} ) is denoted by nano (abbreviated: n). For example, a nanometer (nm) is a billionth of a meter (10 ^{−9} m).
Even when referring to the unit of measurement byte in computer science, the term gigabyte (abbreviated: GB) is understood to mean exactly one billion bytes. That is 10 ^{9} bytes and not 2 ^{30} = 1,073,741,842 bytes, which exceeds one billion bytes by more than seven percent. Today, the name Gibibyte (GiB) is suggested for naming 2 ^{30} bytes ; Gibi (Gi) is a binary prefix while Giga (G) is a decimal prefix.
Difference from American English
In the American-speaking world, billion means billion (often abbreviated as b or bn ). This is to be distinguished from the German trillion , which is 1,000 billion. Such conceptual differences are called false friends .
See also
Web links
Individual evidence
- ↑ Duden | Billion | Spelling, meaning, definition, origin. Retrieved October 15, 2017 .
- ↑ billion. In: Digital dictionary of the German language . Retrieved September 17, 2019
- ↑ billion . In: Meyers Großes Konversations-Lexikon . 6th edition. Volume 13, Bibliographisches Institut, Leipzig / Vienna 1908, p. 843 .
- ↑ Spherical volume calculated for 1 mm diameter multiplied by the density of stainless steel
- ↑ Distance calculator for straight line distance between places , Munich-Rome = 918 km.
- ^ The Economist: The Economist Style Guide: 11th edition . Profile, 2015, ISBN 978-1-78283-091-7 ( google.de [accessed August 19, 2019]).
- ↑ 6.5 Abbreviating 'million' and 'billion' . In: English Style Guide: A handbook for authors and translators in the European Commission , 8th. 1st edition, European Commission , 3 November 2017, p. 32.