《孫子算經卷上》 "Sun Tzŭ's Computational Classic: Volume I"
§4. Names of large numbers

This section introduces a 'long scale' for named powers of ten. Note that the previous section (§3) uses a 'short scale'.

Translation

Chinese source text: Version A, Version B, Version C, Version D.
Unless noted otherwise, I follow the text from Version D, 《知不足齋叢書》本.

Source text Target text Notes
凡大數之法、
萬萬曰億、
萬萬億曰兆、
萬萬兆曰京、
萬萬京曰陔、
萬萬陔曰秭、
萬萬秭曰壤、
萬萬壤曰溝、
萬萬溝曰澗、
萬萬澗曰正、
萬萬正曰載。
[In the] method of all great numbers:
[a] myriad myriad [is] called [a] square-myriad;
[a] myriad myriad square-myriad [is] called [a] multitude;
[a] myriad myriad multitude [is] called [a] capital;
[a] myriad myriad capital [is] called [a] terrace;
[a] myriad myriad terrace [is] called [an] haystack;
[a] myriad myriad haystack [is] called [a] soil;
[a] myriad myriad soil [is] called [a] ditch;
[a] myriad myriad ditch [is] called [a] stream;
[a] myriad myriad stream [is] called [a] right;
[a] myriad myriad right [is] called [a] carry.
  • Version C erroneously has 萬萬澗日正 for 萬萬澗曰正.

Extended commentary

Here we have a 'long scale' where the named quantities go up by a factor of 108:

\begin{aligned} \unit{square-myriad~(億)} &= 10^8 \\ \unit{multitude~(兆)} &= 10^{16} \\ \unit{capital~(京)} &= 10^{24} \\ \unit{terrace~(陔)} &= 10^{32} \\ \unit{haystack~(秭)} &= 10^{40} \\ \unit{soil~(壤)} &= 10^{48} \\ \unit{ditch~(溝)} &= 10^{56} \\ \unit{stream~(澗)} &= 10^{64} \\ \unit{right~(正)} &= 10^{72} \\ \unit{carry~(載)} &= 10^{80}. \end{aligned}

Recall that in the previous section (§3), we had a 'short scale' where the named quantities only went up by a factor of 10.

In modern usage, a 'medium scale' is used where the named quantities go up by a factor of 104. In summary:

Quantity Rendering §3 §4 Modern
億 square-myriad 108 108 108
兆 multitude 109 1016 1012
京 capital 1010 1024 1016
陔 terrace 1011 1032 1020
秭 haystack 1012 1040 1024
壤 soil 1013 1048 1028
溝 ditch 1014 1056 1032
澗 stream 1015 1064 1036
正 right 1016 1072 1040
載 carry 1017 1080 1044

Note that 兆, "multitude", is also used for the SI Prefix mega (106). Confusing eh?

Cite this page

Conway (2023). "Sun Tzŭ's Computational Classic: Volume I §4". <https://yawnoc.github.io/sun-tzu/i/4> Accessed yyyy-mm-dd.