@SergeantQueen, after a person’s ninth birthday, she’s now in her tenth year, which begins when she finishes nine.
She’s in her first year when she’s born, and it stops being her first year when she turns one. Then she’s in her second year.
When we finished our nineteenth century, when it was all over, complete, done, that was at the end of the last day of 1900. The next day began the twentieth. We are now in the 21st, and we’ll reach the end of it when get to 2100.
Suppose you’re in a big auditorium, and there are 100 seats in each row. Start counting at seat number 1. When you get to the end of the first row, you’re at seat number 100. Seat number 101 is the first seat in the second row.