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There are two ways to say "two" in Mandarin Chinese: 二 (èr) or 兩 (traditional form) / 两 (simplified form) (liǎng). These characters cannot be used interchangeably so it's important to know when it is appropriate to use which form.
Here is a guide to understanding which scenario calls for what kind of "two."
With Measure Words
兩 / 两 (liǎng) is used with measure words such as 個 / 个 (ge) or 本 (běn). For example:
兩個人 / 两个人 (liǎng ge rén) - two people
兩本書 / 两本书 (liǎng běn shū) - two books
However, if a measure word is used in conjunction with numbers ending in two, like 22, 102, 542, the 二(èr) form is used. For instance:
二十二個人 / 二十二个人 (èr shí èr ge rén) - twenty-two people
一百零二本書 / 一百零二本书 (yī bǎi líng èr běn shū) - one-hundred and two books
Some numbers will include both kinds of "two." For instance:
兩千兩百零二 / 两千两百零二 (liǎng qiān liǎng bǎi líng èr) - two-thousand, two-hundred and two
二 (èr) is used when counting without measure words. For example:
一, 二, 三 (yī, èr, sān) - one, two, three
十，十一， 十二 (shí, shí yī, shí èr) - ten, eleven, twelve
二十，二十二，二十三 (èr shí, èr shí èr, èr shí sān) - twenty, twenty-one, twenty-two
Counting Measure Word Numbers
Some numbers are also measure words. For example, 百 (bǎi), 千 (qiān), 萬 / 万 (wàn) are measure word numbers. Respectively, the characters mean hundred, thousand, and ten thousand. In those cases, numbers like two-hundred, two-thousand, and twenty-thousand take the 兩 / 两 (liǎng) form:
兩百 / 两百 (liǎng bǎi) - 200
兩千 / 两千 (liǎng qiān) - 2,000
兩萬 / 两万 (liǎng wàn) - 20,000