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10 For 2 ≤ b ≤ 9 the numerical order of the numbers 10 ↑ n b {\displaystyle 10\uparrow ^{n}b} is the lexicographical order with n as the most significant number, so for the numbers of these 8 columns the numerical order is simply line-by-line.
Geo – Grains of sand: All the world's beaches combined have been estimated to hold roughly 10 21 grains of sand. [55] Computing – Manufacturing: Intel predicted that there would be 1.2 × 10 21 transistors in the world by 2015 [56] and Forbes estimated that 2.9 × 10 21 transistors had been shipped up to 2014. [57]
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 example, 10 3 = 1000 and 10 −4 = 0.0001. Exponentiation with base 10 is used in scientific notation to denote large or small numbers. For instance, 299 792 458 m/s (the speed of light in vacuum, in metres per second ) can be written as 2.997 924 58 × 10 8 m/s and then approximated as 2.998 × 10 8 m/s .
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Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. [1] For example, 1 and 1.02 are within an order of magnitude. So are 1 and 2, 1 and 9, or 1 and 0.2.
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