Power of 10

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This article is about the mathematical concept. For other uses, see Power of 10 (disambiguation).
Visualisation of powers of 10 from one to 1 trillion.

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.

NamePowerNumberSI symbolSI prefix
One01
Ten110da(D)deca
Hundred2100h(H)hecto
Thousand31,000k(K)kilo
Ten Thousand (Myriad)410,000
Hundred Thousand5100,000
Million61,000,000Mmega
Billion (Milliard)91,000,000,000Ggiga
Trillion (Billion)121,000,000,000,000Ttera
Quadrillion (Billiard)151,000,000,000,000,000Ppeta
Quintillion (Trillion)181,000,000,000,000,000,000Eexa
Sextillion (Trilliard)211,000,000,000,000,000,000,000Zzetta
Septillion (Quadrillion)241,000,000,000,000,000,000,000,000Yyotta
Octillion (Quadrilliard)271,000,000,000,000,000,000,000,000,000(X)(xona)
Nonillion (Quintillion)301,000,000,000,000,000,000,000,000,000,000(W)?
Decillion (Quintilliard)331,000,000,000,000,000,000,000,000,000,000,000(V)?
Undecillion (Sextillion)361,000,000,000,000,000,000,000,000,000,000,000,000(V)?
Duodecillion (Sextilliard)391,000,000,000,000,000,000,000,000,000,000,000,000,000(V)?
Tredecillion (Septillion)421,000,000,000,000,000,000,000,000,000,000,000,000,000,000(V)?
Quattordecillion (Septilliard)451,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000(V)?
.........
Googol10010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,....??

Negative powers[edit]

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

NamePowerNumberSI symbolSI prefix
Tenth−10.1ddeci
Hundredth−20.01ccenti
Thousandth−30.001mmilli
Ten Thousandth (Myriadth)−40.000 1
Hundred Thousandth−50.000 01
Millionth−60.000 001μmicro
Billionth−90.000 000 001nnano
Trillionth−120.000 000 000 001ppico
Quadrillionth−150.000 000 000 000 001ffemto
Quintillionth−180.000 000 000 000 000 001aatto
Sextillionth−210.000 000 000 000 000 000 001zzepto
Septillionth−240.000 000 000 000 000 000 000 001yyocto
Octillionth−270.000 000 000 000 000 000 000 001(x)(xoni)
Nonillionth−300.000 000 000 000 000 000 000 000 001(w)(wecti)
Decillionth−330.000 000 000 000 000 000 000 000 000 001(v)(vundi)
Undecillionth−360.000 000 000 000 000 000 000 000 000 001(v)(vundi)

Googol[edit]

Main article: googol

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]

Main article: 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 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 spreadsheet 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