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When working with percentages, it's crucial to understand what percent notation means. The word 'percent' originates from the Latin phrase 'per centum,' meaning 'by the hundred.' In essence, a percentage is a fraction with a denominator of 100. For instance, 85.5% means 85.5 out of every 100. This concept makes it easier to handle and convert percentages in mathematical problems.
To write 85.5% as a mathematical fraction, you simply place 85.5 over 100, leading to the fraction: \(\frac{85.5}{100}\). This conversion to fractional form lays the foundation for further simplification.

Once you've converted a percentage to a fraction, the next step is simplifying that fraction. Simplification involves reducing the fraction to its simplest form. To simplify, you must find a common factor that the numerator (top number) and the denominator (bottom number) share. For the fraction \(\frac{85.5}{100}\), both numbers can be divided by 0.5. This simplifies the fraction to \(\frac{171}{200}\). By simplifying fractions, you make them easier to understand and work with in various calculations.
Always look for the greatest common divisor (GCD) when you simplify, which ensures you've reduced the fraction to its most straightforward form. Practicing this helps improve mathematical efficiency and accuracy.

Mathematical conversion is the process of changing numbers from one form to another, like converting percentages to fractions. This skill is essential in many mathematical applications.
Let’s break down the conversion of 85.5% step by step:

• Start with the percent notation: 85.5%.
• Write it as a fraction over 100: \(\frac{85.5}{100}\).
• Simplify the fraction by dividing both the numerator and the denominator by their greatest common factor. For 85.5 and 100, the GCD is 0.5.
• Divide both by 0.5 to get the simplified fraction: \(\frac{171}{200}\).

By mastering these conversion steps, you’ll find it easier to handle various numerical forms and improve your problem-solving abilities.