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A power of 10 is any of the
integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are: : 1, 10,
100 100 or one hundred ( Roman numeral: C) is the natural number following 99 and preceding 101. In medieval contexts, it may be described as the short hundred or five score in order to differentiate the English and Germanic use of "hundred" to de ...
,
1,000 1000 or one thousand is the natural number following 999 (number), 999 and preceding 1001 (number), 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period decimal mark#Digit grouping, separating ...
, 10,000, 100,000, 1,000,000,
10,000,000 10,000,000 (ten million) is the natural number following 9,999,999 and preceding 10,000,001. In scientific notation, it is written as 107. In South Asia except for Sri Lanka, it is known as the crore. In Cyrillic numerals, it is known as the vr ...
. ...


Positive powers

In decimal notation the ''n''th power of ten is written as '1' followed by ''n'' zeroes. It can also be written as 10''n'' or as 1E''n'' in E notation. See order of magnitude and
orders of magnitude (numbers) This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantities and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a ...
for named powers of ten. There are two conventions for naming positive powers of ten, beginning with 109, called the
long and short scales The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the t ...
. Where a power of ten has different names in the two conventions, the long scale name is shown in parentheses. The positive 10 power related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10 prefix-number + 1) × 3/sup> Examples: * billion = 10 2 + 1) × 3/sup> = 109 * octillion = 10 8 + 1) × 3/sup> = 1027


Negative powers

The sequence of powers of ten can also be extended to negative powers. Similar to the positive powers, the negative power of 10 related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10prefix-number + 1) × 3/sup> Examples: * billionth = 102 + 1) × 3/sup> = 10−9 * quintillionth = 105 + 1) × 3/sup> = 10−18


Googol

The number googol is 10100. The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician
Edward Kasner Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in t ...
. It was popularized in Kasner's 1940 book ''
Mathematics and the Imagination ''Mathematics and the Imagination'' is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received s ...
'', where it was used to compare and illustrate very large numbers.
Googolplex A googolplex is the number 10, or equivalently, 10 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 . Written out in ordinary decimal notation, it is 1 fol ...
, a much larger power of ten (10 to the googol power, or 1010100), was also introduced in that book. (Read below)


Googolplex

The number googolplex is 10googol, or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, and was also made by Edward Kasner's nephew. (Read above)


Scientific notation

Scientific notation is a way of writing numbers of very large and very small sizes compactly when precision is less important. A number written in scientific notation has a significand (sometime called a mantissa) multiplied by a power of ten. Sometimes written in the form: : ''m'' × 10''n'' Or more compactly as: : 10''n'' This is generally used to denote powers of 10. Where ''n'' is positive, this indicates the number of zeros after the number, and where the ''n'' is negative, this indicates the number of decimal places before the number. As an example: : 105 = 100,000 : 10−5 = 0.00001 The notation of ''m''E''n'', known as '' E notation'', is used in computer programming, spreadsheets and databases, but is not used in scientific papers.


See also

* Power of two *
Power of three In mathematics, a power of three is a number of the form where is an integer – that is, the result of exponentiation with number three as the base and integer  as the exponent. Applications The powers of three give the place values in ...
* SI prefix * Cosmic View, inspiration for the film ''Powers of Ten'' * Exponentiation *Philip and Phylis Morrison wrote a book called "Powers of Ten: A Book About the Relative Size of Things in the Universe and the Effect of Adding Another Zero" to accompany the video of Eames


Further reading

;Video
Powers of Ten
(1977). Nine-minute film. US '' Public Broadcasting Service (PBS),'' made by
Charles and Ray Eames Charles Eames ( Charles Eames, Jr) and Ray Eames ( Ray-Bernice Eames) were an American married couple of industrial designers who made significant historical contributions to the development of modern architecture and furniture through the work of ...
. "An adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this film transports the viewer to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only as a speck of light among many others. Returning to Earth with breathtaking speed, we move inward - into the hand of the sleeping picnicker - with ten times more magnification every two seconds. Our journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell."


References

{{Large numbers Powers of ten Integer sequences Orders of magnitude