第348課: Large Numbers & 大字
In this lesson, we will learn how to create large numbers greater than 一兆 (one trillion), which we learned about way back in Lesson 33. In addition, we will also learn about a special set of Kanji used to write numerals that were created for a specific goal in mind.
Large Numbers (10^16+)
The method of creating numbers does not change upon reaching the unit for 10^16 – 京（けい）. To get to the next three powers, 十, 百, and 千 are used in that order. After which point, of course, the next unit is introduced. This pattern continues on until 10^71 is reached. In practical application, large numbers are not normally used beyond 10^16, but several of the units are used emphatically in speech to refer to quantities as they are still taught in school.
Chart Note: Just as is the case for the units 万, 億, and 兆, these units are always accompanied with 一 when expressing their respective power of 10.
| 10^# | JPN | ENG | ＋十 | ＋百 | ＋千 |
| 10^16 | 京 （けい） | 10 quadrillion | 十京 10^17 | 百京10^18 | 千京 10^19 |
| 10^20 | 垓 （がい） | 100 quintillion | 十垓 10^21 | 百垓 10^22 | 千垓 10^23 |
| 10^24 | 𥝱 （じょ） 秭 （し） | 1 septillion | 十𥝱・十秭10^25 | 百𥝱・百秭 10^26 | 千𥝱・千秭 10^27 |
| 10^28 | 穣 （じょう） | 10 octillion | 十穣 10^29 | 百穣 10^30 | 千穣 10^31 |
| 10^32 | 溝 （こう） | 100 nonillion | 十溝10^33 | 百溝 10^34 | 千溝 10^35 |
| 10^36 | 澗 （かん） | 1 undecillion | 十澗 10^37 | 百澗 10^38 | 千澗 10^39 |
| 10^40 | 正 （せい） | 10 duodecillion | 十正 10^41 | 百正 10^42 | 千正 10^43 |
| 10^44 | 載 （さい） | 100 tredecillion | 十載 10^45 | 百載 10^46 | 千載 10^47 |
| 10^48 | 極 （ごく） | 1 quindecillion | 十極 10^49 | 百極 10^50 | 千極 千極 10^51 |
| 10^52 | 恒河沙 （こうがしゃ） | 10 sexdecillion | 十恒河沙 10^53 | 百恒河沙 10^54 | 千恒河沙 10^55 |
| 10^56 | 阿僧祇 （あそうぎ） | 100 septemdecillion | 十阿僧祇 10^57 | 百阿僧祇 10^58 | 千阿僧祇 10^59 |
| 10^60 | 那由他 （なゆた） | 1 novemdecillion | 十那由他 10^61 | 百那由他 10^62 | 千那由他 10^63 |
| 10^64 | 不可思議 （ふかしぎ） | 10 vigintillion | 十不可思議10^65 | 百不可思議 10^66 | 千不可思議 10^67 |
| 10^68 | 無量大数 （むりょうたいすう） | 100 unvigintillion | 十無量大数 10^69 | 百無量大数 10^70 | 千無量大数 10^71 |
Note: 秭 is the proper unit and has the ON reading of シ. However, the Kanji itself was miswritten as 𥝱 and given the ON reading of ジョ. What began as a misprint ended up being the standard means of writing this unit, and this remains the case.
Historically speaking, the values associated with these units were unified in the mid-1600s. The system of changing units every fourth power is known as the 万進法.
Before this point, Sino-numerals larger than 万 had varying values based on three separate systems. Initially, 十万 (10^5), 百万 (10^6), and 千万 (10^7) held .the same value as they do today, but a system known as 下数 was devised in which the unit would change after every power of 10 past 万. This resulted in 億 and 兆 having the values 10^5 and 10^6 respectively.
Starting in the Han Dynasty, however, a system known as 上数 was devised in which the next unit would begin after the square of the previous unit was met. In this system, 万万 = 億 (10^8), 億億 = 兆 (10^16), and 兆兆 = 京 (10^32).
Later on, a system known as 中数 was devised in which 千万 (10^7) was followed by 億, and this matched with the current Japanese system up until 千億 (10^11), but the next unit would be every 8 powers. This is known as 万万進. 千億 (10^11), thus, would be followed by 万億 (10^12), 十万億 (10^13), 百万億 (10^14), and 千万億 (10^15). This meant that 兆 stood for 10^16.
Finally, around when larger units were being devised, the 万進法 system utilized by Japan began to appear, and this is of course what Japan ultimately decided to standardize its Sino-Japanese numerals with. In mainland China, however, the 万万進 system has continued to be used in the present.
In the realm of Buddhist texts, units were devised that could go as high as 10^3721838388197764444130659768784964812. This unit is known as 不可説不可説転, and although the number itself is far beyond the realm of practicality or even human comprehension, it and some of the other astronomically large units do happen to be known and utilized in the same way an English speaker might use units like the googolplex. In fact, some units such as 恒河沙 derive from Buddhist texts, but their values are completely different.
大字
When writing numerals in Kanji, more complicated Kanji that are used for their sound in place of the basic Kanji for said number are known as 大字. The purpose of having more complicated means of writing numbers is to prevent counterfeiting or forging totals, which has been incredibly important in banking, accounting, and the judicial system.
If you have ever seen Japanese currency, you will notice that on any bill containing the numbers 1 and 2 that the Kanji 一 and 二 respectively are not used. In both Japan and China, 大字 exist for 0~10 as well as the units 百, 千, and 万. Currently, however, the only ones that are mandated by Japanese law for banknotes are the ones for 1, 2, 3, and 10.
In the chart below, all 大字 that exist in Japan are listed. Forms will be categorized by whether they are 新字体 (new character forms), 旧字体 (old character forms), or 俗字 (informal variants).
| No. | Normal 漢字 | 新字体/Current Form | 旧字体 | 俗字 |
| 0 | 〇 | 零 | ||
| 1 | 一 | 壱 | 壹 | 弌 |
| 2 | 二 | 弐 | 貳 | 貮・弐 |
| 3 | 三 | 参 | 參 | 弎 |
| 4 | 四 | 肆 | ||
| 5 | 五 | 伍 | ||
| 6 | 六 | 陸 | ||
| 7 | 七 | 漆・質 | 柒 | |
| 8 | 八 | 捌 | ||
| 9 | 九 | 玖 | ||
| 10 | 拾 | 拾 | 什 | |
| 100 | 百 | 陌・佰 | ||
| 1000 | 千 | 阡・仟 | ||
| 10000 | 万 | 萬 |