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Power of 10 are we alone in the universe
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 (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:
Contents
- Power of 10 are we alone in the universe
- Power of 10 1st millionaire
- Positive powers
- Negative powers
- Googol
- Scientific notation
- References
Power of 10 1st millionaire
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 (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.
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]
Examples: billion = 10 [(2 + 1) × 3] = 10 9 ; octillion = 10 [(8 + 1) × 3] = 10 27
Negative powers
The sequence of powers of ten can also be extended to negative powers.
Similarly to above, the negative 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]
Examples: billionth = 10 -[(2 + 1) × 3] = 10 -9 ; quintillionth = 10 -[(5 + 1) × 3] = 10 -18
Googol
The number googol is 10100. The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner, popularized in his 1940 book Mathematics and the Imagination, it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 1010100), 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 (sometime called a mantissa) multiplied by a power of ten.
Sometimes written in the form:
m × 10nOr more compactly as:
10nThis is generally used to denote powers of 10. Where n is positive, this indicates the number 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 = 0.00001The notation of mEn, known as E notation, is used in computer programming, spreadsheets and databases, but is not used in scientific papers.