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If you consider the last year of each century, it starts to become a lot more intuitive!
1st century: year 1 to year 100 –>100:100 = 1
2nd century: year 101 to year 200 –> 200:100 = 2
…
20th century: year 1901 to year 2000 –> 2000/100 = 20
21st century: year 2000 to year **2100** –> 2100/100 = 21
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