| Unit conversion procedure (Click Convert to view the procedure) |
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The units of length that were used in Ancient China were tou, thsan, pou, li, kyo, fen, yin (yan), zhang, pou, tchi, cun(tsouen), fen, li, hao, su, and hoe. The base unit was tchi where 1 [tchi] is equal to 0.32 [m] of 0.349956255 [yd]. The largest unit in the length unit system was tou where the length of 1 [tou] is equal to 144000 [m] or 144.000 [km] or 157480.314975 [yd]. The smallest unit in the system was hoe where the length of 1[hoe] is equal to 0.000001[tchi] or \(3.2\cdot 10^{-7}\) [m] or \(3.4995 \cdot 10^{-7}\) [yd]. The table of conversion coefficient is given below.
|
Tou |
Thsan |
Pou |
Li |
Kyo |
fen |
Yin (Yan) |
Zhang |
Pou |
Tchi |
Cun (tsouen) |
Fen |
Li |
Hao |
Su |
Hoe |
|---|
| Tou |
$$1$$ |
$$\frac{25}{8}$$ |
$$25$$ |
$$250$$ |
$$1500$$ |
$$3750$$ |
$$4500$$ |
$$45000$$ |
$$90000$$ |
$$450000$$ |
$$4.5\cdot 10^6$$ |
$$4.5\cdot 10^7$$ |
$$4.5\cdot 10^8$$ |
$$4.5\cdot 10^9$$ |
$$4.5\cdot 10^{10}$$ |
$$4.5\cdot 10^{11}$$ |
| Thsan |
$$\frac{8}{25}$$ |
$$1$$ |
$$8$$ |
$$80$$ |
$$480$$ |
$$1200$$ |
$$1440$$ |
$$14400$$ |
$$28800$$ |
$$14400$$ |
$$1.44\cdot 10^6$$ |
$$1.44\cdot 10^7$$ |
$$1.44\cdot 10^8$$ |
$$1.44\cdot 10^9$$ |
$$1.44\cdot 10^{10}$$ |
$$1.44\cdot 10^{11}$$ |
| Pou |
$$\frac{1}{25}$$ |
$$\frac{1}{8}$$ |
$$1$$ |
$$10$$ |
$$60$$ |
$$150$$ |
$$180$$ |
$$1800$$ |
$$3600$$ |
$$18000$$ |
$$1.8\cdot 10^{5}$$ |
$$1.8\cdot 10^{6}$$ |
$$1.8\cdot 10^{7}$$ |
$$1.8\cdot 10^{8}$$ |
$$1.8\cdot 10^{9}$$ |
$$1.8\cdot 10^{10}$$ |
| Li |
$$\frac{1}{250}$$ |
$$\frac{1}{80}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$6$$ |
$$15$$ |
$$18$$ |
$$180$$ |
$$360$$ |
$$1800$$ |
$$1.8\cdot 10^{4}$$ |
$$1.8\cdot 10^{5}$$ |
$$1.8\cdot 10^{6}$$ |
$$1.8\cdot 10^{7}$$ |
$$1.8\cdot 10^{8}$$ |
$$1.8\cdot 10^{9}$$ |
| Kyo |
$$\frac{1}{1500}$$ |
$$\frac{1}{480}$$ |
$$\frac{1}{60}$$ |
$$\frac{1}{6}$$ |
$$1$$ |
$$\frac{5}{2}$$ |
$$3$$ |
$$30$$ |
$$60$$ |
$$300$$ |
$$3\cdot 10^{3}$$ |
$$3\cdot 10^{4}$$ |
$$3\cdot 10^{5}$$ |
$$3\cdot 10^{6}$$ |
$$3\cdot 10^{7}$$ |
$$3\cdot 10^{8}$$ |
| fen |
$$\frac{1}{3750}$$ |
$$\frac{1}{1200}$$ |
$$\frac{1}{150}$$ |
$$\frac{1}{15}$$ |
$$\frac{2}{5}$$ |
$$1$$ |
$$\frac{6}{5}$$ |
$$12$$ |
$$24$$ |
$$120$$ |
$$1.2\cdot 10^{3}$$ |
$$1.2\cdot 10^{4}$$ |
$$1.2\cdot 10^{5}$$ |
$$1.2\cdot 10^{6}$$ |
$$1.2\cdot 10^{7}$$ |
$$1.2\cdot 10^{8}$$ |
| Yin (Yan) |
$$\frac{1}{4500}$$ |
$$\frac{1}{1440}$$ |
$$\frac{1}{180}$$ |
$$\frac{1}{18}$$ |
$$\frac{1}{3}$$ |
$$\frac{5}{6}$$ |
$$1$$ |
$$10$$ |
$$20$$ |
$$100$$ |
$$10^{3}$$ |
$$10^{4}$$ |
$$10^{5}$$ |
$$10^{6}$$ |
$$10^{7}$$ |
$$10^{8}$$ |
| Zhang |
$$\frac{1}{45000}$$ |
$$\frac{1}{14400}$$ |
$$\frac{1}{1800}$$ |
$$\frac{1}{180}$$ |
$$\frac{1}{30}$$ |
$$\frac{1}{12}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$2$$ |
$$10$$ |
$$10^{2}$$ |
$$10^{3}$$ |
$$10^{4}$$ |
$$10^{5}$$ |
$$10^{6}$$ |
$$10^{7}$$ |
| Pou |
$$\frac{1}{90000}$$ |
$$\frac{1}{28800}$$ |
$$\frac{1}{3600}$$ |
$$\frac{1}{360}$$ |
$$\frac{1}{60}$$ |
$$\frac{1}{24}$$ |
$$\frac{1}{20}$$ |
$$\frac{1}{2}$$ |
$$1$$ |
$$5$$ |
$$50$$ |
$$5\cdot 10^{2}$$ |
$$5\cdot 10^{3}$$ |
$$5\cdot 10^{4}$$ |
$$5\cdot 10^{5}$$ |
$$5\cdot 10^{6}$$ |
| Tchi |
$$\frac{1}{450000}$$ |
$$\frac{1}{144000}$$ |
$$\frac{1}{1800}$$ |
$$\frac{1}{1800}$$ |
$$\frac{1}{300}$$ |
$$\frac{1}{120}$$ |
$$\frac{1}{100}$$ |
$$\frac{1}{10}$$ |
$$\frac{1}{5}$$ |
$$1$$ |
$$10$$ |
$$10^{2}$$ |
$$10^{3}$$ |
$$10^{4}$$ |
$$10^{5}$$ |
$$10^{6}$$ |
| Cun (tsouen) |
$$\frac{1}{4.5\cdot 10^6}$$ |
$$\frac{1}{1.44\cdot 10^6}$$ |
$$\frac{1}{1.8\cdot 10^5}$$ |
$$\frac{1}{1.8\cdot 10^4}$$ |
$$\frac{1}{3\cdot 10^3}$$ |
$$\frac{1}{1.2\cdot 10^3}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{50}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$10$$ |
$$10^{2}$$ |
$$10^{3}$$ |
$$10^{4}$$ |
$$10^{5}$$ |
| Fen |
$$\frac{1}{4.5\cdot 10^7}$$ |
$$\frac{1}{1.44\cdot 10^7}$$ |
$$\frac{1}{1.8\cdot 10^6}$$ |
$$\frac{1}{1.8\cdot 10^5}$$ |
$$\frac{1}{3\cdot 10^4}$$ |
$$\frac{1}{1.2\cdot 10^4}$$ |
$$\frac{1}{10^4}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{5\cdot 10^2}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$10$$ |
$$10^{2}$$ |
$$10^{3}$$ |
$$10^{4}$$ |
| Li |
$$\frac{1}{4.5\cdot 10^8}$$ |
$$\frac{1}{1.44\cdot 10^8}$$ |
$$\frac{1}{1.8\cdot 10^7}$$ |
$$\frac{1}{1.8\cdot 10^6}$$ |
$$\frac{1}{3\cdot 10^5}$$ |
$$\frac{1}{1.2\cdot 10^5}$$ |
$$\frac{1}{10^5}$$ |
$$\frac{1}{10^4}$$ |
$$\frac{1}{5\cdot 10^3}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$10$$ |
$$10^{2}$$ |
$$10^{3}$$ |
| Hao |
$$\frac{1}{4.5\cdot 10^9}$$ |
$$\frac{1}{1.44\cdot 10^9}$$ |
$$\frac{1}{1.8\cdot 10^8}$$ |
$$\frac{1}{1.8\cdot 10^7}$$ |
$$\frac{1}{3\cdot 10^6}$$ |
$$\frac{1}{1.2\cdot 10^6}$$ |
$$\frac{1}{10^6}$$ |
$$\frac{1}{10^5}$$ |
$$\frac{1}{5\cdot 10^4}$$ |
$$\frac{1}{10^4}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$10$$ |
$$10^{2}$$ |
| Su |
$$\frac{1}{4.5\cdot 10^{10}}$$ |
$$\frac{1}{1.44\cdot 10^{10}}$$ |
$$\frac{1}{1.8\cdot 10^9}$$ |
$$\frac{1}{1.8\cdot 10^8}$$ |
$$\frac{1}{3\cdot 10^7}$$ |
$$\frac{1}{1.2\cdot 10^7}$$ |
$$\frac{1}{10^7}$$ |
$$\frac{1}{10^6}$$ |
$$\frac{1}{5\cdot 10^5}$$ |
$$\frac{1}{10^5}$$ |
$$\frac{1}{10^4}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
$$10$$ |
| Hoe |
$$\frac{1}{4.5\cdot 10^{11}}$$ |
$$\frac{1}{1.44\cdot 10^{11}}$$ |
$$\frac{1}{1.8\cdot 10^{10}}$$ |
$$\frac{1}{1.8\cdot 10^9}$$ |
$$\frac{1}{3\cdot 10^8}$$ |
$$\frac{1}{1.2\cdot 10^8}$$ |
$$\frac{1}{10^8}$$ |
$$\frac{1}{10^7}$$ |
$$\frac{1}{5\cdot 10^6}$$ |
$$\frac{1}{10^6}$$ |
$$\frac{1}{10^5}$$ |
$$\frac{1}{10^4}$$ |
$$\frac{1}{10^3}$$ |
$$\frac{1}{10^2}$$ |
$$\frac{1}{10}$$ |
$$1$$ |
The conversion table for ancient Chinese units of length into meters and yards in mathematical form.
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\(\require{cancel} 1 [\mathrm{Tou}] = 1 \cancel{[\mathrm{Tou}]}\cdot \left(450000\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Tou}]}}\right) = 450000 [\mathrm{Tchi}]\)
\(\require{cancel}450000 [\mathrm{Tchi}] = 450000 \cancel{[\mathrm{Tchi}]} \cdot \left(0.32 \frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 144000 [\mathrm{m}]\)
\(\require{cancel} 450000[\mathrm{Tchi}] = 450000\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{tchi}]}}\right) = 157480.31[\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Thsan}] = 1 \cancel{[\mathrm{Thsan}]}\cdot \left(144000\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Thsan}]}}\right) = 144000 [\mathrm{Tchi}]\)
\(\require{cancel} 144000[\mathrm{Tchi}] = 144000 \cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 46080[\mathrm{m}]\)
\(\require{cancel} 144000[\mathrm{tchi}] = 144000\cancel{[\mathrm{tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{tchi}]}}\right) = 50393.7 [\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Pou}] = 1 \cancel{[\mathrm{Pou}]}\cdot \left(18000\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Pou}]}}\right) = 18000[\mathrm{Tchi}]\)
\(\require{cancel} 18000 [\mathrm{Tchi}] = 18000\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 5760 [\mathrm{m}]\)
\(\require{cancel} 18000 [\mathrm{Tchi}] = 18000\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 6299.21[\mathrm{yd}]\)
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\(\require{cancel} 1[\mathrm{Li}] = 1 \cancel{[\mathrm{Li}]}\cdot \left(1800 \frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Li}]}}\right) = 1800 [\mathrm{Tchi}]\)
\(\require{cancel} 1800 [\mathrm{Tchi}] = 1800\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 576[\mathrm{m}]\)
\(\require{cancel} 1800 [\mathrm{Tchi}] = 1800\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 629.92[\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Kyo}] = 1 \cancel{[\mathrm{Kyo}]}\cdot \left(300 \frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Kyo}]}}\right) = 300[\mathrm{Tchi}]\)
\(\require{cancel} 300 [\mathrm{Tchi}] = 300 \cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) =96 [\mathrm{m}]\)
\(\require{cancel} 300 [\mathrm{Tchi}] = 300 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 104.98[\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{fen}] = 120\cancel{[\mathrm{fen}]}\cdot \left(120\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{fen}]}}\right) = 120[\mathrm{Tchi}]\)
\(\require{cancel} 120[\mathrm{Tchi}] = 120\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 38.4[\mathrm{m}]\)
\(\require{cancel} 120[\mathrm{Tchi}] = 120\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 41.99[\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Yin (Yan)}] = 1\cancel{[\mathrm{Yin (Yan)}]}\cdot \left(100 \frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Yin (Yan)}]}}\right) = 100 [\mathrm{Tchi}]\)
\(\require{cancel} 100 [\mathrm{Tchi}] = 100 \cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 32[\mathrm{m}]\)
\(\require{cancel} 100 [\mathrm{Tchi}] = 100 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 34.99 [\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Zhang}] = 1 \cancel{[\mathrm{Zhang}]}\cdot \left(10\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Zhang}]}}\right) = 10[\mathrm{Tchi}]\)
\(\require{cancel} 10 [\mathrm{Tchi}] = 10\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 3.2[\mathrm{m}]\)
\(\require{cancel} 10 [\mathrm{Tchi}] = 10 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) =3.49 [\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Pou}] = 1 \cancel{[\mathrm{Pou}]}\cdot \left(5 \frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Pou}]}}\right) = 5[\mathrm{Tchi}]\)
\(\require{cancel} 5 [\mathrm{Tchi}] = 5\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 1.6[\mathrm{m}]\)
\(\require{cancel} 5 [\mathrm{Tchi}] = 5\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 1.749[\mathrm{yd}]\)
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\(\require{cancel} [\mathrm{Tchi}] = 1 \cancel{[\mathrm{Tchi}]}\cdot \left(1\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Tchi}]}}\right) = 1[\mathrm{Tchi}]\)
\(\require{cancel} 1[\mathrm{Tchi}] = 1\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.32[\mathrm{m}]\)
\(\require{cancel} 1[\mathrm{Tchi}] = 1\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.349[\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Cun (Tsouen)}] = 1 \cancel{[\mathrm{Cun (Tsouen)}]}\cdot \left(0.1\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Cun (Tsouen)}]}}\right) = 0.1 [\mathrm{Tchi}]\)
\(\require{cancel} 0.1 [\mathrm{Tchi}] = 0.1\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0. [\mathrm{m}]\)
\(\require{cancel} 0.1 [\mathrm{Tchi}] = 0.1 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.0349 [\mathrm{yd}]\)
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\(\require{cancel} 1[\mathrm{Fen}] = 1 \cancel{[\mathrm{Fen}]}\cdot \left(\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Fen}]}}\right) = 0.01[\mathrm{Tchi}]\)
\(\require{cancel} 0.01[\mathrm{Tchi}] = 0.01\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.0032[\mathrm{m}]\)
\(\require{cancel} 0.01[\mathrm{Tchi}] = 0.01 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.00349[\mathrm{yd}]\)
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\(\require{cancel} 1[\mathrm{Li}] = 1\cancel{[\mathrm{Li}]}\cdot \left(0.001\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Li}]}}\right) = 0.001[\mathrm{Tchi}]\)
\(\require{cancel} 0.001[\mathrm{Tchi}] = 0.001\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.00032[\mathrm{m}]\)
\(\require{cancel} 0.001[\mathrm{Tchi}] = 0.001\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.000349[\mathrm{yd}]\)
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\(\require{cancel} 1[\mathrm{Hao}] = 1\cancel{[\mathrm{Hao}]}\cdot \left(0.0001\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Hao}]}}\right) = 0.0001[\mathrm{Tchi}]\)
\(\require{cancel} 0.0001[\mathrm{Tchi}] = 0.0001\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.000032[\mathrm{m}]\)
\(\require{cancel} 0.0001[\mathrm{Tchi}] = 0.0001\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 0.0000349[\mathrm{yd}]\)
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\(\require{cancel} 1[\mathrm{Su}] = 1 \cancel{[\mathrm{Su}]}\cdot \left(0.00001 \frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Su}]}}\right) = 0.00001 [\mathrm{Tchi}]\)
\(\require{cancel} 0.00001[\mathrm{Tchi}] = 0.00001\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = [\mathrm{m}]\)
\(\require{cancel} 0.00001[\mathrm{Tchi}] = 0.00001\cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = [\mathrm{yd}]\)
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\(\require{cancel} 1 [\mathrm{Hoe}] = 1\cancel{[\mathrm{Hoe}]}\cdot \left(0.000001\frac{[\mathrm{Tchi}]}{\cancel{[\mathrm{Hoe}]}}\right) = 0.000001[\mathrm{Tchi}]\)
\(\require{cancel} 0.000001[\mathrm{Tchi}] = 0.000001\cancel{[\mathrm{Tchi}]}\cdot \left(0.32\frac{[\mathrm{m}]}{\cancel{[\mathrm{Tchi}]}}\right) = 3.2 \times 10^{-7}[\mathrm{m}]\)
\(\require{cancel} 0.000001[\mathrm{Tchi}] = 0.000001 \cancel{[\mathrm{Tchi}]}\cdot \left(0.349\frac{[\mathrm{yd}]}{\cancel{[\mathrm{Tchi}]}}\right) = 3.49\cdot 10^{-7}[\mathrm{yd}]\)
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