The mathematical basis for decimal to percent conversion lies in the definition of percentage as 'parts per hundred'. This makes the conversion formula both simple and universal.
Mathematical Foundation
If we represent a decimal as d, then the percentage p is given by: p = d × 100. This formula is derived from the fact that 1 = 100%, so any fraction of 1 is that fraction times 100%.
For example, if d = 0.75, then p = 0.75 × 100 = 75%. This means 0.75 is 75/100 or 75 out of every 100 parts.
Advanced Applications
In statistics, decimals representing probabilities (always between 0 and 1) are converted to percentages to make them more intuitive. A probability of 0.025 becomes 2.5%.
In scientific notation, very small or very large decimals are converted to percentages for easier interpretation. For instance, 1.5 × 10⁻⁴ = 0.00015 = 0.015%.
Precision Considerations
When working with repeating decimals like 0.333..., the percentage equivalent is 33.333...%. In practice, we often round to a reasonable number of decimal places.