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Understanding how to convert percentages to fractions is a foundation for working with ratios and proportions in mathematics. Let's break down this process using a simple example: converting 5% into a fraction.

First, recognize that 'percent' means 'out of 100.' So when you see a percentage like 5%, you are actually looking at 5 out of every 100 parts. To express this as a fraction, simply put the percentage number over 100, yielding \( \frac{5}{100} \). But, this doesn't end here; we often need to represent this fraction in its simplest form.

Simplifying the Initial Fraction

In our example, \( \frac{5}{100} \) can be reduced. Since both numerator and denominator are divisible by 5, we divide them to get a simpler equivalent fraction. Through this process, the fraction is reduced to \( \frac{1}{20} \). This simplification step is crucial in mathematics to ease further operations like addition, subtraction, multiplication, or division with other fractions.

Simplifying fractions is about writing a fraction in its most basic form, where the numerator and denominator share no common factors other than 1. This makes calculations easier and results clearer to understand.

Let's employ this process using the fraction we obtained from the percentage 5%, which was \( \frac{5}{100} \). To simplify, look for the greatest common factor (GCF) of the numerator and denominator. In our example, both 5 and 100 are divisible by 5—this is the GCF. Divide both by 5, and you get \( \frac{1}{20} \).

Checking for More Simplifications

Always check if the fraction can be simplified further. If no further division is possible (that is, if the GCF is 1), then you've found your simplest form. In our case, 1 and 20 have no other common factors, so \( \frac{1}{20} \) is as simple as it gets.

The process of converting percentages to decimals is straightforward and is based on the understanding that 'percent' means 'per hundred.' To convert a percentage into a decimal, the decimal point is moved two places to the left.

For instance, converting the percentage 5% to a decimal involves moving the decimal point two positions to the left. Start with the percent value, 5.0%, and translate it to 0.05. Remember that the '%' sign is replaced by the decimal point in this process.

Why Move Two Places?

The reason behind moving the decimal two places is because you're effectively dividing by 100 (as previously discussed, percent means per hundred). This division by 100 adjusts the value to represent the proportion as a part of one, rather than a part of hundred, which is what the decimal system is based on.