Oh, dude, the year 762 CE would totally be in the 8th century. Like, I know it's confusing with all those numbers, but just think about it - 762 is closer to 800 than it is to 700. So, yeah, 8th century it is.
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The 15th century. It was the last year of it.
The first century CE began at the beginning of 1 CE and ended at the end of 100 CE. The first century BCE ended at the end of 1 BCE, and the second century CE began at the beginning of 101 CE. (Note that there is no year 0, so 1 BCE immediately precedes 1 CE.)
The 8th Century AD, which is also the 8th Century CE.
the year 1000 AD or CE
The eighth. Remember that there is no zeroth century. The first century is 1 through 100 CE, so the count of centuries is always 1 higher than the hundreds place of the year.