The ancient Chinese units of weight were Da (shih), Tan, Jun (kwan), Jin (tchin), Liang, Zhu, and Shu. The based weight unit was Jin (tchin) were 1 [Jin (tchin)] is equal to 0.596816 [kg]. The largest unit was Dan (shih) where 1 [Dan (shih)] is equal to 120 [Jin (tchin)] or 71.61792 [kg] or 157.92[lb]. The smallest unit is Shu where 1[Shu] is equal to 0.000026[Jin (tchin)] or 0.000015542[kg] or 0.00003427 [lb]. in the following table, a list of conversion factors between weight units is given.
|
Dan (shih) |
Tan |
Jun (kwan) |
Jin (tchin) |
Liang |
Zhu |
Shu |
| Dan (shih) |
$$1$$ |
$$\frac{6}{5}$$ |
$$4$$ |
$$120$$ |
$$1920$$ |
$$46080$$ |
$$4608000$$ |
| Tan |
$$\frac{5}{6}$$ |
$$1$$ |
$$\frac{10}{3}$$ |
$$100$$ |
$$1600$$ |
$$38400$$ |
$$3840000$$ |
| Jun (kwan) |
$$\frac{1}{4}$$ |
$$\frac{3}{10}$$ |
$$1$$ |
$$30$$ |
$$480$$ |
$$11520$$ |
$$1152000$$ |
| Jin (tchin) |
$$\frac{1}{120}$$ |
$$\frac{1}{100}$$ |
$$\frac{1}{30}$$ |
$$1$$ |
$$16$$ |
$$384$$ |
$$38400$$ |
| Liang |
$$\frac{1}{1920}$$ |
$$\frac{1}{1600}$$ |
$$\frac{1}{480}$$ |
$$\frac{1}{16}$$ |
$$1$$ |
$$24$$ |
$$2400$$ |
| Zhu |
$$\frac{1}{46080}$$ |
$$\frac{1}{38400}$$ |
$$\frac{1}{11520}$$ |
$$\frac{1}{384}$$ |
$$\frac{1}{24}$$ |
$$1$$ |
$$100$$ |
| Shu |
$$\frac{1}{4608000}$$ |
$$\frac{1}{3840000}$$ |
$$\frac{1}{1152000}$$ |
$$\frac{1}{38400}$$ |
$$\frac{1}{2400}$$ |
$$\frac{1}{100}$$ |
$$1$$ |
The procedure of converting any weight unit into Jin (tchin) and then to kilograms and pounds is shown below.
|
$$\require{cancel} 1 [\mathrm{Dan (shih)}] = 1\cancel{\left[\mathrm{Dan (shih)}\right]}\cdot \left(120\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Dan (shih)}\right]}}\right) = 120\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 120[\mathrm{Jin (tchin)}] = 120\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 71.61792\left[\mathrm{kg}\right]$$
$$\require{cancel} 120[\mathrm{Jin (tchin)}] = 120\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 157.92\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1[\mathrm{Tan}] = 1\cancel{\left[\mathrm{Tan}\right]}\cdot \left(100\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Tan}\right]}}\right) = 100\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 100[\mathrm{Jin (tchin)}] = 100\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 59.6816\left[\mathrm{kg}\right]$$
$$\require{cancel} 100[\mathrm{Jin (tchin)}] = 100\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 131.6\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1[\mathrm{Jun (kwan)}] = 1\cancel{\left[\mathrm{Jun (kwan)}\right]}\cdot \left(30\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Jun (kwan)}\right]}}\right) = 30\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 30[\mathrm{Jin (tchin)}] = 30\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 17.90448\left[\mathrm{kg}\right]$$
$$\require{cancel} 30[\mathrm{Jin (tchin)}] = 30\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 39.48\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1[\mathrm{Jin (tchin)}] = 1\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 1\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 1[\mathrm{Jin (tchin)}] = 1\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.596816\left[\mathrm{kg}\right]$$
$$\require{cancel} 1[\mathrm{Jin (tchin)}] = 1\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 1.316\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1[\mathrm{Liang}] = 1\cancel{\left[\mathrm{Liang}\right]}\cdot \left(0.0625\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Liang}\right]}}\right) = 0.0625\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 0.0625[\mathrm{Jin (tchin)}] = 0.0625\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.037301\left[\mathrm{kg}\right]$$
$$\require{cancel} 0.0625[\mathrm{Jin (tchin)}] = 0.0625\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.08225\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1[\mathrm{Zhu}] = 1\cancel{\left[\mathrm{Zhu}\right]}\cdot \left(0.0026\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Zhu}\right]}}\right) = 0.0026\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 0.0026[\mathrm{Jin (tchin)}] = 0.0026\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.001554\left[\mathrm{kg}\right]$$
$$\require{cancel} 0.0026[\mathrm{Jin (tchin)}] = 0.0026\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.003427\left[\mathrm{lb}\right]$$
|
|
$$\require{cancel} 1 [\mathrm{Shu}] = 1\cancel{\left[\mathrm{Shu}\right]}\cdot \left(0.000026\frac{\left[\mathrm{Jin (tchin)}\right]}{\cancel{\left[\mathrm{Shu}\right]}}\right) = 0.000026\left[\mathrm{Jin (tchin)}\right]$$
$$\require{cancel} 0.000026[\mathrm{Jin (tchin)}] = 0.000026\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(0.596816\frac{\left[\mathrm{kg}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.00001554\left[\mathrm{kg}\right]$$
$$\require{cancel} 0.000026[\mathrm{Jin (tchin)}] = 0.000026\cancel{\left[\mathrm{Jin (tchin)}\right]}\cdot \left(1.316\frac{\left[\mathrm{lb}\right]}{\cancel{\left[\mathrm{Jin (tchin)}\right]}}\right) = 0.00003427\left[\mathrm{lb}\right]$$
|
No comments:
Post a Comment