Are You in the Correct Century?

Someone asked me if it were true that I had researched a family back to the 17th century. I responded that I only had the family back to the mid-1700s. The 1700s are not the 17th century, they are the 18th century. In a similar fashion, the 1800s are the 19th century, the 1900s are the 20th century, etc.

The problem?

The 1st century was those years from year 1 through year 100.

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