percent is *per cent*, or “per 100”.
When you divide one number by another and get a decimal, you’re getting how much out of 1 that number is. Such as 13/20=0.65/1. Multiply top and bottom by 100 and you get 65/100, or 65 per 100; 65%.
Another way to think about it is that 1 is a whole. When you divide 13 by 20, you’re saying that 20 parts makes up one whole. So whatever your decimal is, that’s how much of one whole you have. Similarly, you multiply by 100 (top and bottom) to get what that part of the whole would be when one whole is 100 parts.