The word 'century' as in the 21st century, can be very confusing. Century means 100 years. (cent = 100). The first century was from 1AD to 101 AD (there is no year "0"). The second century was from 101 AD to 200 AD, and so on. So, in 2005, we are in the 21st century, which lasts from

2001 - 2100 AD.

Often, we will use approximate time, not a specific date. We might say the early 19th century, which would mean from about 1801 to 1820. Or, we might say the middle 19th century which would mean from about 1840 to 1860. So, the late 19th century might be from 1880 to 1890.

Students sometimes get confused about decades as well. A decade means 10 years. If you hear someone talk about the 1960s, they are talk about the 10-year span between 1960 and 1969. Likewise, the 2010s, our current decade, refers to the years between 2010 and 2019.