Powers 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 (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:
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
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
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 is a way of writing numbers of very large and very small sizes compactly when precision is less important.
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