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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.
In the base ten number system, integer powers of 10 are written as the digit 1 followed or preceded by a number of zeroes determined by the sign and magnitude of the exponent. For example, 10 3 = 1000 and 10 −4 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers.
Because superscript exponents like 10 7 can be inconvenient to display or type, the letter "E" or "e" (for "exponent") is often used to represent "times ten raised to the power of", so that the notation m E n for a decimal significand m and integer exponent n means the same as m × 10 n.
Engineering notation or engineering form (also technical notation) is a version of scientific notation in which the exponent of ten is always selected to be divisible by three to match the common metric prefixes, i.e. scientific notation that aligns with powers of a thousand, for example, 531×10 3 instead of 5.31×10 5 (but on calculator displays written without the ×10 to save space).
[10] The following is a list of all currently known Mersenne primes and perfect numbers, along with their corresponding exponents p . As of 2024 [update] , there are 52 known Mersenne primes (and therefore perfect numbers), the largest 18 of which have been discovered by the distributed computing project Great Internet Mersenne Prime Search ...
In this way, numbers up to 10 3·999+3 = 10 3000 (short scale) or 10 6·999 = 10 5994 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if n is 9 or smaller. For larger n (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy. [17]
To compare numbers in scientific notation, say 5×10 4 and 2×10 5, compare the exponents first, in this case 5 > 4, so 2×10 5 > 5×10 4. If the exponents are equal, the mantissa (or coefficient) should be compared, thus 5×10 4 > 2×10 4 because 5 > 2.
10 −15: 1 femtohertz (fHz) ~3 fHz: Sound waves created by a supermassive black hole in the Perseus cluster [1] 10 −14: 10 fHz ~31.71 fHz: Once every one million years 10 −12: 1 picohertz (pHz) 1.23 pHz Precession of the Earth's axis (about every 25,700 years) 10 −11: 10 pHz ~31.71 pHz: Once per millennium 10 −10: 100 pHz ~317.1 pHz ...
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