What is defined as the percent change in a value compared to its initial value?

The term that refers to the percent change in a value compared to its initial value is known as percentage change. This measurement quantifies how much a value has increased or decreased relative to its original amount and is calculated using the formula:

[

\text{Percentage Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\text{Initial Value}} \right) \times 100%

]

Percentage change is particularly useful in various scientific and mathematical contexts as it provides a clear way to express the magnitude of change relative to the starting point. This allows for the comparison of changes across different scales since it standardizes the change as a portion of the initial value.

In contrast, the other terms like percentage difference and fractional change have different meanings. Percentage difference typically measures how much two values differ from each other as a percentage of their average, while fractional change focuses on the proportion of increase or decrease without converting it to a percentage. Relative change is a broader term that can sometimes refer to similar calculations but is not exclusively defined in the same way as percentage change. Therefore, for measuring a change in a value relative to its starting point, percentage change is the most accurate term to use.