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When solving percent problems, the goal is to find how large one quantity is in relation to another on a scale of 100. In mathematical terms, percent means 'per hundred,' hence the symbol \(\%\). The basic formula for percentage is \( \frac{part}{whole} = \frac{percent}{100} \).

So, in the context of the exercise, where we have the question '148.8 is what percent of 960?', we are essentially looking for the part (148.8) as a percentage of the whole (960). By setting up the equation \( \frac{148.8}{960} = x \), we establish the relationship between the part and the whole. The variable \(x\) represents the unknown percentage we are trying to find. To solve for \(x\), we divide 148.8 by 960 and obtain a decimal, which we then convert into a percent. This operation uncovers the proportion of 148.8 with respect to 960 in percentage terms.

Conversion between decimals and percents is a crucial skill in understanding the relationship between different representations of ratios. To convert a decimal to a percent, you simply multiply the decimal by 100 and add the percent sign. This process translates the decimal value into the percentage form, which is more intuitive for comparison and analysis in many real-life scenarios.

In our example, the decimal value following the division is 0.155. To convert this decimal to a percent, we use the conversion formula: \(0.155 \times 100 = 15.5\%\). This tells us that the number 148.8 is 15.5% of 960. The multiplication by 100 scales up the decimal by two decimal places, effectively shifting the decimal point two places to the right to arrive at the percentage.

Mathematical formulas are predefined relationships between quantities that express a principle or concept used for solving mathematical problems. In the case of percent problems, the formula takes on a simple structure, capturing the part-whole relationship used to determine percentages. The step-by-step process of solving the exercise utilizes the percent equation formula: \( \frac{part}{whole} = \frac{percent}{100} \).

This formula underpins many calculations involving percentages, whether finding a percentage, the part, or the whole. For this specific problem, our focus is on finding the percent. The formula provides a framework to set up an equation and proceed to isolate the variable of interest, which in this case is the percentage value \(x\). Following the steps to solve for \(x\) allows the student to determine the exact percent represented by 148.8 in relation to 960.