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One million hu makes six zi|original: 秭; a number representing 10⁴⁰ in this system grains of millet.
Ten million hu makes six rang|original: 壤; 10⁴⁸ grains of millet.
One hundred million hu makes six gou|original: 溝; 10⁵⁶ grains of millet.
The text is demonstrating the staggering scale of the grain economy by multiplying the 60 million grains found in a single "hu" by ever-larger factors.
One billion hu makes six jian|original: 澗; 10⁶⁴ grains of millet.
Ten billion hu makes six zheng|original: 正; 10⁷² grains of millet.
[One hundred billion hu] makes six zai|original: 載; 10⁸⁰ grains of millet.
The method for calculating Large Numbers is as follows:
Ten thousand times ten thousand is called yi 10⁸; unlike the modern Western million, ancient Chinese large numbers often scaled by factors of 10,000.
Ten thousand times ten thousand yi is called zhao 10¹⁶.
Ten thousand times ten thousand zhao is called jing 10²⁴.
Ten thousand times ten thousand jing is called gai 10³².
Ten thousand times ten thousand gai is called zi 10⁴⁰.
Ten thousand times ten thousand zi is called rang 10⁴⁸.
Ten thousand times ten thousand rang is called gou 10⁵⁶.
Ten thousand times ten thousand gou is called jian 10⁶⁴.
Ten thousand times ten thousand jian is called zheng 10⁷².
Ten thousand times ten thousand zheng is called zai 10⁸⁰.
For a circle, the circumference is three and the diameter is one. original: 周三徑一; This is a traditional Chinese approximation of Pi (π ≈ 3). While recognized as imprecise by some scholars of the era, it remained a standard for practical engineering and tax assessment.
For a square, the side is five and the diagonal is seven. original: 方五邪七; An approximation for the square root of 2 (√2 ≈ 1.4). In a perfect square with a side of 5, the diagonal is actually 7.07, so 7 was a close functional estimate.
When the diagonal is known and the side is sought: multiply the diagonal by five and divide by seven.
When the side is known and the diagonal is sought: multiply the side by seven and divide by five.
A cubic inch of gold weighs one jin|original: 斤; often translated as a "catty" or "pound," roughly 600 grams in the medieval period.
A cubic inch of silver weighs fourteen liang|original: 兩; "taels" or ounces. Since sixteen liang traditionally make one jin, this indicates that silver was considered roughly 12.5% less dense than gold in this standardized system.