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Percentage calculation is a fundamental aspect of math that deals with representing numbers as a fraction of 100. It's a versatile tool used in various fields such as finance, statistics, and everyday life scenarios like calculating discounts or understanding statistics presented in percentages.

In the context of the exercise, calculating 0.075% of 625 involves understanding that 'percent' means 'per hundred.' Therefore, 0.075% is the same as 0.075 per 100, or mathematically expressed as \(0.075/100\). To calculate this percentage of 625, you multiply by the whole (625) which translates to \(0.075/100 \times 625\). Simplifying this expression will give you the part of 625 that is equal to 0.075%.

When it comes to solving percentages, it's important to grasp the three components involved in any percentage problem: the percentage, the part, and the whole. These components have a definite relationship: the part is what percentage of the whole.

To solve for any of these components, we use the basic percentage formula: \( \text{percentage} = \frac{\text{part}}{\text{whole}} \times 100\). In our exercise, we knew the percentage (0.075%) and the whole (625) and were solving for the part. By rearranging the formula \( \text{part} = \text{percentage} \times \frac{\text{whole}}{100}\), we can insert our known values to find the unknown 'part'. This systematic approach to solving percentage problems is essential to ensure accuracy and understanding.

Cross-multiplication is an effective mathematical technique used to solve equations that involve two ratios or fractions being equal. It's particularly useful in percentage problems to find a missing value when the other values are known.

The process involves multiplying the numerator of one fraction by the denominator of the other fraction and setting these products equal to each other. For the given exercise, this method applied to the basic percent equation takes the form of: \(0.075 \times 625 = \text{part} \times 100\). By simplifying and solving this equation, you will find the value of the 'part' we are looking for. The beauty of cross-multiplication lies in its ability to handle proportions and percentages efficiently, making it a go-to method in percentage calculations.