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Mathematics portal

1,000,000,000 (one billion, short scale; one thousand million or milliard, long scale) is the natural number following 999,999,999 and preceding 1,000,000,001.

In scientific notation, it is written as 10⁹.

A billion traditionally equated to one million, million, (1,000,000,000,000) though the short scale (American English) billion of merely one thousand million (1,000,000,000) has been adopted in finance and increasingly in other fields. The unambiguous term thousand million has the same meaning in both scales.

In South Asian English, it is known as 100 crore or 1 arab.

The term milliard can also be used to refer to 1,000,000,000; this name very often appears in other languages.

This terminology is rarely used in English outside of British English. The SI prefix giga indicates 1,000,000,000 times the base unit.

See Orders of magnitude (numbers) for larger numbers; and long and short scales.

Selected 10-digit numbers (1,000,000,000–9,999,999,999)[link]

Visualisation of powers of ten from one to 1 billion

• 1023456789 – smallest pandigital number in base 10
• 1026753849 – smallest pandigital square that includes 0
• 1073676287 – 15th Carol number
• 1073741824 = 2³⁰
• 1073807359 – 14th Kynea number
• 1129760415 – 23rd Motzkin number
• 1134903170 – 45th Fibonacci number
• 1162261467 = 3¹⁹
• 1220703125 = 5¹³
• 1234567890 – pandigital number with the digits in order
• 1311738121 – 25th Pell number
• 1382958545 – 15th Bell number
• 1406818759 – 30th Wedderburn–Etherington number
• 1836311903 – 46th Fibonacci number
• 1882341361 – The least prime whose reversal is both square (40391²) and triangular (triangular of 57121).
• 1977326743 = 7¹¹
• 2147483647 – 8th Mersenne prime and the largest signed 32-bit integer
• 2147483648 = 2³¹
• 2214502422 – 6th primary pseudoperfect number
• 2357947691 = 11⁹
• 2971215073 – 11th Fibonacci prime (47th Fibonacci number)
• 3166815962 – 26th Pell number
• 3192727797 – 24th Motzkin number
• 3323236238 – 31st Wedderburn–Etherington number
• 3405691582 – hexadecimal CAFEBABE; used as a placeholder in programming.
• 3405697037 – hexadecimal CAFED00D; used as a placeholder in programming.
• 3486784401 = 3²⁰
• 4294836223 – 16th Carol number
• 4294967291 – Largest prime 32-bit unsigned integer
• 4294967295 – Maximum 32-bit unsigned integer (hexadecimal FFFFFFFF)
• 4294967296 = 2³²
• 4294967297 – the first composite Fermat number
• 4295098367 – 15th Kynea number
• 4807526976 – 48th Fibonacci number
• 5784634181 – 13th alternating factorial
• 6103515625 = 5¹⁴
• 6210001000 – only self-descriptive number in base 10
• 6227020800 = 13!
• 6983776800 – 15th colossally abundant number
• 7645370045 – 27th Pell number
• 7778742049 – 49th Fibonacci number
• 7862958391 – 32nd Wedderburn–Etherington number
• 8589869056 – 6th perfect number
• 8589934592 = 2³³
• 9043402501 – 25th Motzkin number
• 9814072356 – largest square pandigital number, largest pandigital pure power
• 9876543210 – largest pandigital number without redundant digits

Sense of scale[link]

The facts below give a sense of how large 1,000,000,000 (10⁹) is in the context of time according to current scientific evidence:

• 10⁹ seconds is 114 days short of 32 calendar years (≈ 31.7 years).
• About 10⁹ minutes ago, the Roman Empire was flourishing and Christianity was emerging. (10⁹ minutes is roughly 1,900 years.) A billion minutes ago, Trajan was emperor in Rome^[1].
• About 10⁹ hours ago, modern human beings and their ancestors were living in the Stone Age (more precisely, the Middle Paleolithic). (10⁹ hours is roughly 114,000 years.)
• About 10⁹ days ago, Australopithecus, an ape-like creature related to an ancestor of modern humans, roamed the African savannas. (10⁹ days is roughly 2.7 million years.)
• About 10⁹ months ago, dinosaurs walked the Earth during the late Cretaceous. (10⁹ months is roughly 82 million years.)
• About 10⁹ years ago, the first multicellular eukaryotes appeared on Earth.
• The universe is currently thought to be about 13.7 × 10⁹ years old.

In terms of distance:

• 10⁹ inches is 15,783 miles (25,400 km), more than halfway around the world and sufficient to reach any point on the globe from any other point.
• 10⁹ metres is almost three times the distance from the Earth to the Moon.
• 10⁹ kilometres is over six times the distance from the Earth to the Sun.

In terms of finance:

• The possession of assets with total value of 10⁹ United States dollars would place a person among the world's wealthiest individuals.
• As visualized in a work by artist Michael Marcovici, this amount of money in stacks of hundred-dollar bills can fit on twelve wrapped pallets.^[2]

In terms of area:

• A billion square inches would be a square about one half mile on a side.
• A piece of finely woven bed sheet cloth that contained a billion holes would measure about 500 square feet (46 m²), large enough to cover a moderate sized apartment.

In terms of volume:

• There are a billion cubic millimeters in a cubic meter.
• A billion grains of table salt or granulated sugar would occupy a volume of about two and a half cubic feet.
• A billion cubic inches would be a volume comparable to a large commercial building slightly larger than a typical supermarket.

In terms of natural landscape; a small mountain, slightly larger than Stone Mountain Georgia, United States, would weigh (have a mass of) a billion tons.

In terms of count:

A is a cube; B consists of 1000 cubes of type A. C consists of 1000 Bs; and D 1000 Cs. Thus there are 1 million As in C; and 1,000,000,000 As in D.

References[link]

Look up million in Wiktionary, the free dictionary.

One million (1,000,000) or one thousand thousand, is the natural number following 999,999 and preceding 1,000,001. The word is derived from the early Italian millione (milione in modern Italian), from mille, "thousand", plus the augmentative suffix -one.^[1]

In scientific notation, it is written as 1×10⁶ or just 10⁶.^[2] Physical quantities can also be expressed using the SI prefix mega, when dealing with SI units. For example, 1 megawatt equals 1,000,000 watts.

The meaning of the word "million" is common to the short scale and long scale numbering systems, unlike the larger numbers, which have different names in the two systems.

The million is sometimes used in the English language as a metaphor for a very large number, as in "Never in a million years" and "You're one in a million", or a hyperbole, as in "I've walked a million miles" and "You've asked the million-dollar question".

Visualisation of powers of ten from 1 to 1 million

Visualizing one million[link]

Even though it is often stressed that counting to precisely a million would be an exceedingly tedious task due to the time and concentration required, there are many ways to bring the number "down to size" in approximate quantities, ignoring irregularities or packing effects.

• Information: Not counting spaces, the text printed on 136 pages of an Encyclopædia Britannica, or 600 pages of pulp paperback fiction contains approximately one million characters.
• Length: There are one million millimeters in a kilometer, and roughly a million sixteenths of an inch in a mile. A typical car tire might rotate a million times in a 1,200-mile (1,900 km) trip, while the engine would do several times that number of revolutions.
• Fingers: If the width of a human finger is 2.2225 cm (7/8 inch), then a million fingers lined up would cover a distance of approximately 22 km (14 mi). If a person walks at a speed of 4 km/h, it would take them approximately five and a half hours to reach the end of the fingers.
• Area: A square a thousand objects or units on a side contains a million such objects or square units, so a million holes might be found in less than three square yards of window screen, or similarly, in about one half square foot (400–500 cm²) of bed sheet cloth. A city lot 70 by 100 feet is about a million square inches.
• Volume: The cube root of one million is only one hundred, so a million objects or cubic units is contained in a cube only a hundred objects or linear units on a side. A million grains of table salt or granulated sugar occupies only about 64 ml, slightly over a quarter of a cup, the volume of a cube one hundred grains on a side. One million cubic inches would be the volume of a small room only 8 1/3 feet long by 8 1/3 feet wide by 8 1/3 feet high.
• Mass: A million cubic millimeters (small droplets) of water would have a volume of (one litre) and a mass of one kilogram. A million millilitres or cubic centimetres (one cubic metre) of water has a mass of a million grams or one tonne.
• Weight: A million 80 milligram Honey bees would weigh the same as an 80 kg person.
• Landscape: A pyramidal shaped hill 600 feet (180 m) wide at the base and 100 feet (30 m) high would weigh about a million tons.
• Computer: A display resolution of 1,280 by 800 pixels contains 1,024,000 pixels.
• Money: A USD bill of any denomination weighs 1 gram. There are 454 grams in a pound. One million $1 bills would weigh in at 2,204.62 pounds, or just over 1 ton.
• Time: 1 million seconds are 11.57 days.

In Indian English, it may be known as 10 lakhs.

1,000,000 pixels (Resized; click to enlarge to original size).

Selected 7-digit numbers (1,000,000 – 9,999,999)[link]

• 1,000,003 – Smallest 7-digit prime number
• 1,046,527 – Carol number
• 1,048,576 = 2²⁰ (power of two), 2,116-gonal number, an 8,740-gonal number and a 174,764-gonal number, the number of bytes in a mebibyte, the number of kibibytes in a gibibyte, and so on. Also the most rows that Calc ^[3] (OpenOffice.org Calc 3.3) can accept in a single worksheet.
• 1,048,976 – Leyland number
• 1,050,623 – Kynea number
• 1,058,576 – Leyland number
• 1,084,051 – Keith number
• 1,089,270 – harmonic divisor number
• 1,136,689 – Pell number, Markov number
• 1,234,567 – Smarandache consecutive number (base 10 digits are in numerical order)
• 1,278,818 – Markov number
• 1,346,269 – Fibonacci number, Markov number
• 1,413,721 – square triangular number
• 1,421,280 – harmonic divisor number
• 1,441,440 – colossally abundant number
• 1,441,889 – Markov number
• 1,539,720 – harmonic divisor number
• 1,563,372 – Wedderburn-Etherington number
• 1,594,323 = 3¹³
• 1,596,520 – Leyland number
• 1,647,086 – Leyland number
• 1,679,616 = 6⁸
• 1,686,049 – Markov number
• 1,741,725 – equal to the sum of the seventh power of its digits
• 1,771,561 = 11⁶ = 121³ = 1331², also, Commander Spock's estimate for the tribble population in the Star Trek episode "The Trouble With Tribbles"
• 1,941,760 – Leyland number
• 1,953,125 = 5⁹
• 2,012,174 – Leyland number
• 2,012,674 - Markov number
• 2,097,152 = 2²¹, power of two
• 2,097,593 - prime Leyland number
• 2,124,679 - Wolstenholme prime
• 2,178,309 - Fibonacci number
• 2,356,779 - Motzkin number
• 2,423,525 - Markov number
• 2,674,440 - Catalan number
• 2,744,210 - Pell number
• 2,796,203 - Wagstaff prime
• 2,922,509 - Markov number
• 3,263,442 - product of the first five terms of Sylvester's sequence
• 3,263,443 - sixth term of Sylvester's sequence
• 3,276,509 - Markov number
• 3,301,819 - alternating factorial
• 3,524,578 - Fibonacci number, Markov number
• 3,626,149 - Wedderburn-Etherington number
• 3,628,800 = 10! (factorial of ten)
• 4,037,913 - sum of the first ten factorials
• 4,190,207 - Carol number
• 4,194,304 = 2²², power of two
• 4,194,788 - Leyland number
• 4,198,399 - Kynea number
• 4,208,945 - Leyland number
• 4,210,818 - equal to the sum of the seventh powers of its digits
• 4,213,597 - Bell number
• 4,400,489 - Markov number
• 4,782,969 = 3¹⁴
• 4,785,713 - Leyland number
• 4,826,809 = 13⁶
• 5,134,240 - the largest number that cannot be expressed as the sum of distinct fourth powers
• 5,702,887 - Fibonacci number
• 5,764,801 = 7⁸
• 5,882,353 = 588² + 2353²
• 6,536,382 - Motzkin number
• 6,625,109 - Pell number, Markov number
• 7,453,378 - Markov number
• 7,861,953 - Leyland number
• 7,913,837 - Keith number
• 8,000,000 - Used to represent infinity in Japanese mythology
• 8,388,608 = 2²³, power of two
• 8,389,137 - Leyland number
• 8,399,329 - Markov number
• 8,436,379 - Wedderburn-Etherington number
• 8,675,309 - A hit song for Tommy Tutone (also a twin prime)
• 8,675,311 - A twin prime
• 8,946,176 - self-descriptive number in base 8
• 9,227,465 - Fibonacci number, Markov number
• 9,369,319 - Newman–Shanks–Williams prime
• 9,647,009 - Markov number
• 9,694,845 - Catalan number
• 9,765,625 = 5¹⁰
• 9,800,817 - equal to the sum of the seventh powers of its digits
• 9,865,625 - Leyland number
• 9,926,315 - equal to the sum of the seventh powers of its digits
• 9,999,991 - Largest 7-digit prime number

See also[link]

• Huh (god), depictions of whom were also used in hieroglyphs to represent one million
• Megagon
• Names of large numbers
• Orders of magnitude (numbers) to help compare dimensionless numbers between 1,000,000 and 10,000,000 (10⁶ and 10⁷).

References[link]