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Understanding how to convert percentages to decimals is a fundamental skill in mathematics and everyday life. It's often required in financial calculations, data analysis, and even when grading exams. Here's a simple way to perform this conversion: divide the percentage value by 100. This approach works because the word 'percent' literally means 'per hundred,' which is why 100% equals 1, as it represents a whole. Let's apply this to an example.

To convert a percentage like 75% to a decimal, divide 75 by 100, which gives you 0.75. In a more complex scenario, where the percentage is not a whole number—take, for instance, 0.75%—the same principle applies. Divide 0.75 by 100, resulting in a decimal of 0.0075. When dealing with smaller percentages like these, it's crucial to remember the placement of the decimal point to ensure accuracy.

Fractions are another form of representing numbers, just like percentages and decimals. To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number). This can be easily done with a calculator or by long division. For example, the fraction \( \frac{3}{4} \) can be converted to a decimal by dividing 3 by 4, yielding 0.75.

When converting fractions that represent percentages (like \( \frac{3}{4} \% \) in our exercise), it's a two-step process. After converting \( \frac{3}{4} \) to 0.75, you then need to convert this percentage to a decimal by following the process described in the previous section. This highlights the interconnectedness between fractions and percentages, and understanding this relationship is essential for accurate mathematical calculations.

Mathematical problem-solving requires a systematic approach to break down complex problems into more manageable steps. The ability to convert percentages to decimals and fractions to decimals showcases this principle well. It first starts with comprehending the individual concepts—knowing what a fraction, a percentage, and a decimal represent—and then applying a methodical process to convert between these forms.

In the given exercise, we start by converting the fraction \( \frac{3}{4} \) to a decimal. After that, we tackle the conversion of a percentage to a decimal. This two-step problem-solving process is a common structure in mathematics that increases in complexity with more advanced problems. Whether dealing with simple conversions or complex equations, the ability to break down a problem into clear, approachable steps is a key component of successful mathematical problem-solving.