What is a percentage or a percent? One clue is in the name itself: per-cent. We frequently use the word per to compare or divide quantities, as in rates and ratios, and the leftover word cent means centum or one hundred in Latin. The term percent refers to a quantity expressed as a fraction (per) whose denominator is 100 (cent).

For example, we can write 0.5 = \frac{1}{2} = \frac{50}{100} = 50 \%. We pronounce the percentage symbol, %, percent. Isn't it telling that it looks a lot like our division symbol \div?

We see percentages all the time in the real world – frequently in sales at stores. During a sale, a store might mark their shirts 50% down so that a $20 shirt now costs $10. A week later, the store may announce customers can take an additional 20% off the sale price. How do you determine the new discounted price of the shirt? (Try it!)

As another example, we can say that 15/100 is 15% or that 0.25 is 25%.
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