Editing 2319: Large Number Formats
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| 10^13.4024 ''(title text)'' | | 10^13.4024 ''(title text)'' | ||
| A person who has come back to numbers after a journey deep into some random theoretical field | | A person who has come back to numbers after a journey deep into some random theoretical field | ||
β | | In some fields of mathematics, especially those dealing with very {{w|large numbers}}, numbers are sometimes represented by raising ten (or some other convenient base) to an oddly precise power, to facilitate comparison of their magnitudes without filling up pages upon pages of digits. An example of this is {{w|Skewes's number}}, which is formally calculated to be ''e''<sup>''e''<sup>''e''<sup>79</sup></sup></sup>, but is more commonly approximated as 10<sup>10<sup>10<sup>34</sup></sup></sup>. 13.4024 is a rounded version of the {{w|common logarithm}} of 25,259,974,097,204 (log<sub>10</sub> 25,259,974,097,204 = 13.4024329009); thus, this "format" is still mathematically correct, but uncommon. However, only by using many more digits will the result get close enough to be rounded to the original number 10^13.40243290087302 = 25,259,974,097,203.5, which would round up to the correct number. The number from the title text, 10^13.4024 = 25,258,060,548,319.6, differs from | + | | In some fields of mathematics, especially those dealing with very {{w|large numbers}}, numbers are sometimes represented by raising ten (or some other convenient base) to an oddly precise power, to facilitate comparison of their magnitudes without filling up pages upon pages of digits. An example of this is {{w|Skewes's number}}, which is formally calculated to be ''e''<sup>''e''<sup>''e''<sup>79</sup></sup></sup>, but is more commonly approximated as 10<sup>10<sup>10<sup>34</sup></sup></sup>. 13.4024 is a rounded version of the {{w|common logarithm}} of 25,259,974,097,204 (log<sub>10</sub> 25,259,974,097,204 = 13.4024329009); thus, this "format" is still mathematically correct, but uncommon. However, only by using many more digits will the result get close enough to be rounded to the original number 10^13.40243290087302 = 25,259,974,097,203.5, which would round up to the correct number. The number from the title text, 10^13.4024 = 25,258,060,548,319.6, differs from theoriginal number by over a billion. |
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