Editing 2319: Large Number Formats
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==Explanation== | ==Explanation== | ||
− | This comic shows | + | {{incomplete|Created by ABRAHAM LINCOLN. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.}} |
+ | This comic shows how different people express large numbers. This number in question is approximately the distance from the planet Earth to the planet Jupiter as of June 2020, in {{w|inch|inches}} (1 inch = 2.54 cm). | ||
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{| class="wikitable" | {| class="wikitable" | ||
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| 25,259,974,097,204 | | 25,259,974,097,204 | ||
| Normal Person | | Normal Person | ||
− | | This is the full number | + | | This is the full number, written out in the normal fashion, with commas to indicate powers of 1000. Note that this convention is only considered normal in the Anglo-Saxon world; conventions for writing large numbers in full vary considerably across cultures. For example, in countries where the comma is used as a {{w|decimal separator}} (including Europe outside the UK), one would write the number as 25.259.974.097.204 (or 25'259'974'097'204 in Switzerland, or 25 259 974 097 204 in Poland). Under the {{w|Indian numbering system}}, this number would be written as 25,25,997,40,97,204. |
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| 25 Trillion | | 25 Trillion | ||
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| 25 Billion | | 25 Billion | ||
| Old British Person | | Old British Person | ||
− | | In current English usage, across the | + | | In current English usage, across the anglophonic world with some hold-outs, an n-illion means 10^(3n+3) as per the {{w|short scale}} system popularised by American influence in international trade, so a trillion means 10^12, as above. However, older British English use had an n-illion meaning 10^(6n) (i.e. the simpler calculation of ''million^n''), so a billion meant 10^12. The change stems from a 1974 commitment by Harold Wilson, the Prime Minister of the UK at the time, to change from the {{w|long scale}} (previously often described as the British system) to the short one for all official purposes. |
Though not instantly widely adopted for common usage, the mid-'70s could therefore be considered the key turning point between when an older or younger British person learns (as the change filters through the system at various stages of education) what their "Billion"s and "Trillion"s are supposed to represent. | Though not instantly widely adopted for common usage, the mid-'70s could therefore be considered the key turning point between when an older or younger British person learns (as the change filters through the system at various stages of education) what their "Billion"s and "Trillion"s are supposed to represent. | ||
− | As well as 'traditionalist' British use, the | + | (The 1971 transition to decimalised currency may also date a person's experiences, but was a more comprehensive and immediate change for everyone who handled any money at all, in the UK, and thus was a more definite point of change apart from the extended survival of the "12 times table" being taught by rote in primary education, rather than ending at the 10s.) |
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+ | As well as 'traditionalist' British use, the Long Scale is widely used in the non-anglophone world, in local language versions, though while the British system tended to infill n-and-a-half powers of the million with the term "thousand n-illion", the suffix "-illi''ard''", or equivalent, is often used for the thousands multiple directly atop the respective "-illion" point. | ||
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− | |2. | + | |2.526x10<sup>13</sup> |
|Scientist | |Scientist | ||
|This number is formatted in {{w|scientific notation}}, using the exponent 10<sup>13</sup>. | |This number is formatted in {{w|scientific notation}}, using the exponent 10<sup>13</sup>. | ||
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− | | 2. | + | | 2.525997x10<sup>13</sup> |
| Scientist trying to avoid rounding up | | Scientist trying to avoid rounding up | ||
− | | Using as many decimal places as necessary until hitting a digit (0-4) that results in rounding down, even if it goes against the common scientific practice of reporting the correct amount of "significant figures". | + | | Using as many decimal places as necessary until hitting a digit (0-4) that results in rounding down, even if it goes against the common scientific practice of reporting the correct amount of "significant figures". A previous version of the comic had a typo (the number was ''2.5997x10<sup>13</sup>''), but Randall updated the comic. |
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| 2.526e13 or | | 2.526e13 or | ||
2.526*10^13 | 2.526*10^13 | ||
| Software developer | | Software developer | ||
− | | | + | | Computer code cannot typically use the superscripts or other types of rich text formatting, so the exponent is indicated with the {{w|caret}}. "e13" is {{w|Scientific notation#E notation|(scientific) E notation}} for the expression "10 raised to the power of 13". |
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| 25,259,973,541,888 | | 25,259,973,541,888 | ||
| Software developer who forgot about floats | | Software developer who forgot about floats | ||
− | | | + | | This is the number after being converted to the limited precision of a {{w|32-bit floating point|32-bit float}}. |
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| 10<sup>13</sup> | | 10<sup>13</sup> | ||
| Astronomer | | Astronomer | ||
− | | For extremely large distances, astronomers typically only care about orders of magnitude, e. | + | | For extremely large distances, astronomers typically only care about orders of magnitude, i.e. 10<sup>13</sup>, not 10<sup>12</sup> or 10<sup>14</sup>. Randall often jokes about the lack of precision needed by astronomers, such as in that one xkcd (#[[2205]]) where the astronomer-cosmologist is equally willing to make pi equal to one, or ten. The original number is rounded to the nearest power of ten. |
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| {∅,{∅},{∅,{∅}},{∅,{∅},{... | | {∅,{∅},{∅,{∅}},{∅,{∅},{... | ||
| Set theorist | | Set theorist | ||
− | | | + | | In {{w|Zermelo–Fraenkel set theory}}, the natural numbers are defined recursively by letting 0 = ∅ (the {{w|empty set}}), and ''n'' + 1 = ''n'' ∪ {''n''}. So, every natural number ''n'' is the set of all natural numbers less than ''n'', and since 0 is defined as the empty set, all numbers are nested sets of empty sets. This notation is a bit unpractical for large numbers - without the ellipsis, the expression would reach much farther than to Jupiter. |
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| 1,262,998,704,860 score and four | | 1,262,998,704,860 score and four | ||
| Abraham Lincoln | | Abraham Lincoln | ||
− | | In the {{W|Gettysburg Address}}, Lincoln speaks the number "87" as "four score and seven" ("score" meaning "20"). | + | | In the {{W|Gettysburg Address}}, Lincoln speaks the number "87" as "four score and seven" ("score" meaning "20"). Here, the original number is rewritten in "score" (multiples of 20) plus a remainder (four). |
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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 | ||
− | | 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 | + | | 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 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 to use, but is not commonly used. |
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==Transcript== | ==Transcript== | ||
− | :[A panel only with text. At the top there is four lines of explanatory text. Below that are | + | {{incomplete transcript|Do NOT delete this tag too soon.}} |
+ | :[A panel only with text. At the top there is four lines of explanatory text. Below that there are 5 rows of number formats. There are 2 columns in each row. Each numerical format is in red, with black text explaining the format below it.] | ||
− | :<big>What the way you write large numbers says about you</big> | + | :<big>What the way you write large</big> |
− | :(Using the approximate current distance to Jupiter in inches as an example) | + | :<big>numbers says about you</big> |
+ | :(Using the approximate current distance | ||
+ | :to Jupiter in inches as an example) | ||
− | :<span style="color: | + | :[First row:] |
+ | :<span style="color:red">25,259,974,097,204</span> | ||
:Normal person | :Normal person | ||
− | + | :<span style="color:red">25 trillion</span> | |
− | :<span style="color: | ||
:Normal person | :Normal person | ||
− | :<span style="color: | + | :[Second row:] |
+ | :<span style="color:red">25 billion</span> | ||
:Old British person | :Old British person | ||
− | + | :<span style="color:red">2.526x10<sup>13</sup></span> | |
− | :<span style="color: | ||
:Scientist | :Scientist | ||
− | :<span style="color: | + | :[Third row:] |
+ | :<span style="color:red">2.525997x10<sup>13</sup></span> | ||
:Scientist trying to avoid rounding up | :Scientist trying to avoid rounding up | ||
− | + | :<span style="color:red">2.526e13 or<br>2.526*10^13</span> | |
− | :<span style="color: | ||
:Software developer | :Software developer | ||
− | :<span style="color: | + | :[Fourth row:] |
+ | :<span style="color:red">25,259,973,541,888</span> | ||
:Software developer who forgot about floats | :Software developer who forgot about floats | ||
− | + | :<span style="color:red">10<sup>13</sup></span> | |
− | :<span style="color: | ||
:Astronomer | :Astronomer | ||
− | :<span style="color: | + | :[Fifth row:] |
+ | :<span style="color:red">{∅,{∅},{∅,{∅}},{∅,{∅},{...</span> | ||
:Set theorist | :Set theorist | ||
− | + | :<span style="color:red">1,262,998,704,860<br>score and four</span> | |
− | :<span style="color: | ||
:Abraham Lincoln | :Abraham Lincoln | ||
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics with color]] | [[Category:Comics with color]] | ||
− | [[Category:Programming]] | + | [[Category: Programming]] |
− | [[Category:Math]] | + | [[Category: Math]] |
− | [[Category:Astronomy]] | + | [[Category: Astronomy]] |
− | [[Category:Science]] | + | [[Category: Science]] |
[[Category:Comics featuring politicians]] | [[Category:Comics featuring politicians]] | ||
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