Power of 10

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Visualisation of powers of ten from one to 1 billion.

In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times. By definition, the number one is a power (the zeroth power) of ten. The first few powers of ten are:

1, 10, 100, 1000, 10000, 100000, 1000000, 1000000000 ... (sequence A011557 in OEIS)

Positive powers[edit]

In decimal notation the nth power of ten is written as '1' followed by n zeroes. It can also be written as 10n or as 1En in E notation. See order of magnitude and orders of magnitude (numbers) for named powers of ten. There are two conventions for naming positive powers of ten, called the long and short scales. Where a power of ten has different names in the two conventions, the long scale name is shown in brackets.

Name Power Number SI symbol SI prefix
One 0 1
Ten 1 10 da deca
Hundred 2 100 h hecto
Thousand 3 1,000 k kilo
Ten Thousand (Myriad) 4 10,000
Hundred Thousand 5 100,000
Million 6 1,000,000 M mega
Billion (Milliard) 9 1,000,000,000 G giga
Trillion (Billion) 12 1,000,000,000,000 T tera
Quadrillion (Billiard) 15 1,000,000,000,000,000 P peta
Quintillion (Trillion) 18 1,000,000,000,000,000,000 E exa
Sextillion (Trilliard) 21 1,000,000,000,000,000,000,000 Z zetta
Septillion (Quadrillion) 24 1,000,000,000,000,000,000,000,000 Y yotta
Octillion (Quadrilliard) 27 1,000,000,000,000,000,000,000,000,000
Nonillion (Quintillion) 30 1,000,000,000,000,000,000,000,000,000,000
Decillion (Quintilliard) 33 1,000,000,000,000,000,000,000,000,000,000,000
... ... ...
Googol 100 1,000,000,000,000,000,000,000,000,000,000,000,000,000,....

Negative powers[edit]

The sequence of powers of ten can also be extended to negative powers:

Name Power Number SI symbol SI prefix
Tenth −1 0.1 d deci
Hundredth −2 0.01 c centi
Thousandth −3 0.001 m milli
Myriad −4 0.000 1
Hundred Thousandth −5 0.000 01
Millionth −6 0.000 001 μ micro
Billionth −9 0.000 000 001 n nano
Trillionth −12 0.000 000 000 001 p pico
Quadrillionth −15 0.000 000 000 000 001 f femto
Quintillionth −18 0.000 000 000 000 000 001 a atto
Sextillionth −21 0.000 000 000 000 000 000 001 z zepto
Septillionth −24 0.000 000 000 000 000 000 000 001 y yocto
Octillionth −27 0.000 000 000 000 000 000 000 001 --- ---

Googol[edit]

The number googol is 10100. The term was coined in 1938 by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Popularized by his 1940 book Mathematics and the Imagination, it was used to compare and illustrate really large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 1010100), was also introduced in that book.

The name of this power of ten inspired the name of the company Google.

Scientific notation[edit]

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 mantissa multiplied by a power of ten.

Sometimes written in the form:

a × 10b

Or more compactly as:

10b

This is generally used to denote powers of 10. Where b is positive, this indicates the number zeros after the number, and where the b is negative, this indicates the number of decimal place before the number.

As an example:

105 = 100,000[1]
10−5 = 0.00001[2]

The notation of aEb is used in excel databases but not used in scientific papers.

See also[edit]

References[edit]

  1. ^ http://www.mathsteacher.com.au/year7/ch02_power/08_pow10/pow.htm
  2. ^ http://hesperia.gsfc.nasa.gov/sftheory/power10.htm