Power of 10
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:
| 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 | 4 | 10,000 | ||
| hundred thousand | 5 | 100,000 | ||
| million | 6 | 1,000,000 | M | mega |
| ten million | 7 | 10,000,000 | ||
| hundred million | 8 | 100,000,000 | ||
| billion | 9 | 1,000,000,000 | G | giga |
| trillion | 12 | 1,000,000,000,000 | T | tera |
| quadrillion | 15 | 1,000,000,000,000,000 | P | peta |
| quintillion | 18 | 1,000,000,000,000,000,000 | E | exa |
| sextillion | 21 | 1,000,000,000,000,000,000,000 | Z | zetta |
| septillion | 24 | 1,000,000,000,000,000,000,000,000 | Y | yotta |
| octillion | 27 | 1,000,000,000,000,000,000,000,000,000 | ||
| nonillion | 30 | 1,000,000,000,000,000,000,000,000,000,000 | ||
| decillion | 33 | 1,000,000,000,000,000,000,000,000,000,000,000 | ||
| undecillion | 36 | 1,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| duodecillion | 39 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| tredecillion | 42 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| 45 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | |||
| quindecillion | 48 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| sexdecillion | 51 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| septendecillion | 54 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| octodecillion | 57 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| novemdecillion | 60 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| vigintillion | 63 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
| googol | 100 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 |
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 | 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 | 0.000 000 000 000 000 000 000 000 001 | ||
| nonillionth | −30 | 0.000 000 000 000 000 000 000 000 000 001 | ||
| decillionth | −33 | 0.000 000 000 000 000 000 000 000 000 000 001 | ||
| undecillionth | −36 | 0.000 000 000 000 000 000 000 000 000 000 000 001 | ||
| duodecillionth | −39 | 0.000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| tredecillionth | −42 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| quattuordecillionth | −45 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| quindecillionth | −48 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| sexdecillionth | −51 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| septendecillionth | −54 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| octodecillionth | −57 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| novemdecillionth | −60 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
| vigintillionth | −63 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 |
Googol
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 when precision is less important.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 mEn, known as E notation, is used in computer programming, spreadsheets and databases, but is not used in scientific papers.