In mathematics, a percentage is a number or ratio as a fraction of 100. It is often denoted using the percent sign, “%”, or the abbreviation “pct.”
For example, 45% (read as “forty-five percent”) is equal to 45/100, or 0.45. A related system which expresses a number as a fraction of 1000 uses the terms “per mil” and “millage”. Percentages are used to express how large/small one quantity is, relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity, which should be greater than zero. For example, an increase of $ 0.15 on a price of $ 2.50 is an increase by a fraction of 0.15/2.50 = 0.06. Expressed as a percentage, this is therefore a 6% increase.
Although percentages are usually used to express numbers between zero and one, any ratio can be expressed as a percentage. For instance, 111% is 1.11 and −0.35% is −0.0035. Although this is technically inaccurate as per the definition of percent, an alternative wording in terms of a…