Power of 10

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 of ten. The first few non-negative powers of ten are:

Positive powers

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 for named powers of ten. There are two conventions for naming positive powers of ten, beginning with 10⁹, 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 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
Examples:

billion = 10 = 10⁹
octillion = 10 = 10²⁷

Name	Alternate names	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	lakh	5	100,000
million		6	1,000,000	M	mega
ten million	crore	7	10,000,000
hundred million		8	100,000,000
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	...	E	exa
sextillion	trilliard	21		Z	zetta
septillion	quadrillion	24		Y	yotta
octillion	quadrilliard	27		R	ronna
nonillion	quintillion	30		Q	quetta
decillion	quintilliard	33
vigintillion	decilliard	63
googol		100
centillion		303
googolplex		10

For further examples, see Names of large numbers. Numbers larger than about a trillion are rarely referred to by name or written out as digits, but instead are typically described with exponent notation.

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:
10⁻
Examples:

billionth = 10⁻ = 10⁻⁹
quintillionth = 10⁻ = 10⁻¹⁸

Name	Power	Number	SI symbol	SI prefix
one	0	1
tenth	−1	0.1	d	deci
hundredth	−2	0.01	c	centi
thousandth	−3	0.001	m	milli
ten-thousandth	−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	...	f	femto
quintillionth	−18		a	atto
sextillionth	−21		z	zepto
septillionth	−24		y	yocto
octillionth	−27		r	ronto
nonillionth	−30		q	quecto
decillionth	−33
googol-minutia	-100

Googol and googolplex

The number googol is 10¹⁰⁰. The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. It was popularized in Kasner's 1940 book Mathematics and the Imagination, where it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten, was also introduced in that book.

Scientific notation

Scientific notation is a way of writing numbers of very large and very small sizes compactly.
A number written in scientific notation has a significand multiplied by a power of ten.
Sometimes written in the form:
Or more compactly as:
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:
The notation of mE''n, known as E notation'', is used in computer programming, spreadsheets and databases, but is not used in scientific papers.