In Chinese, the translated names of SI units depends on whether you are in mainland China or in Taiwan.

普通話 Pǔtōnghuà (Mainland China)

Putonghua translates the SI base unit and each of the prefixes; it then applies them according to the standard rules.

  • wēi micro-
  • háo milli-
  • centi-
  • fēn deci-
  • shí deca-
  • bǎi hecto-
  • qiān kilo-

The base units are:

  • metre
  • shēng litre
  • gram (but kilogram is jīn)

. Applying the prefixes you have:

  • 微米 wēimǐ micrometre (micron)
  • 毫米 háomǐ millimetre
  • 厘米 límǐ centimetre
  • 分米 fēnmǐ decimetre
  • mǐ (or 公米 gōngmǐ) metre
  • 十米 shímǐ decametre
  • 百米 bǎimǐ hectometre
  • 千米 qiānmǐ kilometre (but more usually 公里 gōnglǐ)

Square measures are prefixed 平方 píngfāng: e.g., 平方分米 square centimetre. Cubic measures are prefixed 立方 lìfāng: e.g., 立方分米 cubic centimetre. Volumes are similar. However weights are not so straightforward:

  • 亳克 háokè milligram
  • 厘克 líkè decigram
  • gram
  • 十克 shíkè decagram
  • 百克 bǎikè hectogram
  • 公斤 gōngjīn kilogram
  • 公擔 gōngdàn quintal
  • 千斤 qiānjīn (or dūn) metric ton

國語 Guóyǔ (Taiwan)

Taiwan uses the word 公 gōng (short for 公制計量單位 gōngzhì jìliàng dānwèi, which is the name for the International System of Units) prefixed to the nearest equivalent traditional Chinese unit.

  • 公釐 gōnglí (also written 公厘) millimetre (abbrev. 粍)
  • 公分 gōngfēn centimetre (abbrev. 糎)
  • 公寸 gōngcùn decimetre (abbrev. 籿)
  • 公尺 gōngchǐ metre (abbrev. 粎; transliterated as 米突 mǐtú)
  • 公丈 gōngzhàng decametre (abbrev. 粀 or 籵)
  • 公引 gōngyǐn hectometre (abbrev. 粌 or 粨)
  • 公里 gōnglǐ kilometre (abbrev. 粁)

The abbreviations do not have a single syllable pronunciation (although Unicode gives a fallacious one). Amazingly, my Taiwanese dictionary gives ㄇㄧㄌㄧㄇㄝㄊㄜㄦ 'millimetre' as one of the the standard pronunciations for 粍—and so forth. I can only presume the influence of Japanese in this.

Volumes and liquid measure are constructed likewise (with a few additional words where there is no equivalent or near equivalent Chinese weight)

  • 公撮 gōngcuō millilitre
  • 公勺 gōngsháo centilitre
  • 公合 gōnggě decilitre
  • 公升 gōngshēng litre
  • 公斗 gōngdǒu decalitre
  • 公石 gōngshí hectolitre
  • 公秉 gōngbǐng kilolitre
  • 公絲 gōngsī milligram
  • 公毫 gōngháo centigram
  • 公銖 gōngzhū decigram
  • 公克 gōngkè (or 公分 gōngfēn) gram
  • 公錢 gōngqián decagram
  • 公兩 gōngliǎng hectogram
  • 公斤 gōngjīn kilogram
  • 公衡 gōnghéng myriagram
  • 公擔 gōngdàn quintal
  • 公噸 gōngdūn metric ton

市制計量單位 Chinese Weights and Measures

The precise values of each of these units has changed from dynasty to dynasty. Their current values are as follows:–

長度 Length

  • lí (also written )
  • fēn (= 10)
  • cùn (= 10) = 3.33 cm
  • chǐ (= 10) = 333 cm
  • zhàng (= 10) = 3.33 m
  • yǐn (= 10)
  • lǐ (= 15) = 0.5 km

容量 Volume and liquid measure

  • cuō = 1 ml
  • sháo (= 10)
  • gě (= 10)
  • shēng (= 10)
  • dǒu (= 10) = 1 l
  • shí (= 10)

重量 Weight

  • sī (= 10)
  • háo (= 10)
  • fēn (= 10)
  • qián (= 10) = 5 g
  • liǎng (= 10) = 50 g
  • jīn (= 10) = 500 g
  • dàn (= 100)

Chinese Weights and Measures (until the end of the 戰國 Warring States period circa 256 BC)

長度 Length

  • cùn = 2.25cm
  • zhǐ (= 8) = 18.0 cm
  • chǐ (= 10) = 22.5 cm
  • bù (= 6) = 1.13 m
  • rèn (= 7) = 1.58 m
  • xún (= 8) = 1.80 m
  • zhàng (= 10) = 2.25 m
  • lǐ (= 300) = 405 m

容量 Volume and liquid measure

  • gě = 19.4 ml
  • shēng (= 10) = 194 ml
  • dòu (= 4) = 776 ml
  • dǒu (= 10) = 1.94 l
  • hú (= 10) = 19.4 l
  • zhōng (= 256) = 49.66 l

圭 guī, 撮 cuō and 抄 chāo are three ancient measures, the value of which are disputed. There is conflicting evidence from different sources.
《孫子算經》 Sūnzǐ Suàn Jīng gives 圭 = 64 黍、圭 = 6 粟、撮 = 10 圭、抄 = 10 撮。
《隋書》 Suì Shū gives 圭 = 6 粟、抄 = 10 圭、撮 = 10 抄。
《夏侯陽算經》 Xià Hóuyáng Suàn Jīng gives 圭 = 10 粟。

重量 Weight

  • zhū = 0.67 g
  • liǎng (= 10) = 16 g
  • jīn (= 16) = 256 g
  • jūn (= 30) = 7.68 kg

References:
《最新現代漢語大詞典》新加坡:世界書局(1992)。
《辭海》臺灣:鐘文出版社(民國八十九年)。
小川環樹《新字源》東京:角川(1969)。

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