# billion

billion
1000000000
presentation
dual 11 1011 1001 1010 1100 1010 0000 0000
Octal 73 4654 5000
Duodecimal 2 3AA9 3854
Morse code - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Mathematical properties
sign positive
parity straight
Factorization ${\ displaystyle 2 ^ {9} \ cdot 5 ^ {9}}$ Divider All figures extending through the term with be represented. (All dividers see running text) ${\ displaystyle 2 ^ {n} \ cdot 5 ^ {m}, n, m \ in \ mathbb {N} _ {0}}$ ${\ displaystyle \ max (n, m) \ leq 9}$ 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: ${\ displaystyle 2 ^ {9} \ cdot 5 ^ {9}}$ ${\ displaystyle (9 + 1) \ cdot (9 + 1)}$ ${\ displaystyle (10 \ cdot 10 = 100)}$ ${\ displaystyle 2 ^ {0}}$ ${\ displaystyle 2 ^ {9}}$ ${\ displaystyle 5 ^ {0}}$ ${\ displaystyle 5 ^ {9}}$ 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 .