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In both scales, names are given to orders of magnitude at increments of 1000. Both systems use the same names for magnitudes less than 10 9. Differences arise from the use of identical names for larger magnitudes. For the same magnitude name (n-illion), the value is 10 3n+3 in the short scale but 10 6n in the long scale for positive integers n ...
The naming procedure for large numbers is based on taking the number n occurring in 10 3n+3 (short scale) or 10 6n (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix -illion. In this way, numbers up to 10 3·999+3 = 10 3000 (short scale) or 10 6·999 = 10 5994 (long scale
The following table lists the names of small numbers used in the long and short scales, along with the power of 10, ... 1×10 −∞: Zero –1 –1 ...
It can be seen that the order of magnitude is included in the number name in this example, because bi- means 2, tri- means 3, etc. (these make sense in the long scale only), and the suffix -illion tells that the base is 1 000 000. But the number names billion, trillion themselves (here with other meaning than in the first chapter) are not names ...
One of the most common choices is the logarithmic scale, which is a representation of the positive numbers on a line, such that the distance of two points is the unit length, if the ratio of the represented numbers has a fixed value, typically 10. In such a logarithmic scale, the origin represents 1; one inch to the right, one has 10, one inch ...
To put in perspective the size of a googol, the mass of an electron, just under 10 −30 kg, can be compared to the mass of the visible universe, estimated at between 10 50 and 10 60 kg. [5] It is a ratio in the order of about 10 80 to 10 90, or at most one ten-billionth of a googol (0.00000001% of a googol).
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1/52! chance of a specific shuffle Mathematics: The chances of shuffling a standard 52-card deck in any specific order is around 1.24 × 10 −68 (or exactly 1 ⁄ 52!) [4] Computing: The number 1.4 × 10 −45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.