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In this exercise, you are asked to find out what number 10.4% of a whole is equal to 52. The process begins by applying the basic percent equation. This involves understanding that 'percent' means 'per hundred'. Therefore, when you encounter a percentage like 10.4%, think of it as 10.4 out of every 100 parts. To solve this, you express 10.4% as a fraction in the form \[\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\]Here, the 'Part' of the equation is 52, the 'Whole' is the number we are seeking, and the percentage given is 10.4. This is how you set up the equation: \[0.104 \times \text{Whole} = 52\]You multiply 0.104 (the percentage in decimal form) by the 'Whole' to find what part equals 52.

To perform any percentage calculation correctly, you need to convert the percentage into a decimal. This is a crucial step in solving the given exercise. Converting 10.4% into a decimal makes the calculations manageable by allowing you to perform simple multiplication and division operations.
To convert a percentage like 10.4% into its decimal equivalent, divide by 100: \[10.4\% = \frac{10.4}{100} = 0.104\]Remember this method whenever you need to convert percentages into easier-to-handle decimal numbers. This process—dividing the percentage by 100—transforms complex percentage problems into more straightforward calculation tasks.

Once you have set up the initial equation using the basic percent logic \[0.104 \times \text{Whole} = 52\], the next step is to isolate the unknown variable, 'Whole'. This requires rearranging the equation, a fundamental part of algebraic operations.
To isolate 'Whole', you need to get rid of the 0.104 multiplying it. Do this by performing the opposite operation—division. Therefore, divide both sides of the equation by 0.104: \[\text{Whole} = \frac{52}{0.104}\]Rearranging equations correctly is a key skill in mathematics, as it allows you to solve for unknown variables by simplifying the given information.

With the equation rearranged to \[\text{Whole} = \frac{52}{0.104}\], the final step is performing the division to solve for 'Whole'. This computation provides the exact number that 10.4% makes 52.
When computing, ensure accuracy by carefully carrying out the division. Using a calculator can help, especially with decimals involved: \[52 \div 0.104 = 500\]Performing this operation confirms that the 'Whole', the number we were searching for, is 500. Accurate computation is vital, as it guarantees the correctness of mathematical solutions and ensures that problem-solving yields the intended result.