Final answer:
A percent is always a fraction with a denominator of 100, and this is true by its very definition. Converting between decimals, fractions, and percents involves working with this base-100 system, where the percent symbol (%) indicates the quotient out of 100.
Step-by-step explanation:
A percent is always a fraction whose denominator is 100. By definition, a percent is a way of expressing a number as a fraction out of 100. If we take 25%, for example, it is the same as 25/100, which can also be simplified to 1/4. This shows that the percent symbol (%) represents the concept that the number preceding the % sign is out of 100. To convert a decimal to a percent, the decimal is written as a fraction, and if necessary, converted into a fraction with a denominator of 100, which can then be written as a percent.
Similarly, converting percents to fractions involves writing the value of the percent as a fraction with a denominator of 100 and then simplifying as needed. Hence, the statement that a percent is a fraction whose denominator is always 100 is true. This understanding is crucial when performing percentage calculations, which involve taking a part as compared to the whole (which is standardized at 100), and is commonly used in various situations like calculating discounts, determining concentration, and scoring tests.