The abbreviation of Taiwan Dollar is TWD or NTD.

The biggest number is 2000TWD. However, I suggest to exchange to 1000TWD because the most people are using is 1000.

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The cheapest and most convenient way is to do exchange at the airport.

There are 2 banks at the airport which are Bank of Taiwan and Mega Bank. The rate is similar so you can do exchange in any of them.
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https://www.megabank.com.tw/other/bulletin02_02.asp
To see above link, you will know the exchange fee is only 2%.
And you need to pay additional 100TWD per exchange.
Therefore, it is recommended to exchange your money to TWD once at the airport.