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Turning a decimal into a fraction is a fundamental step in many math problems. To begin, understand that a decimal shows a part of a whole number. For example, the decimal 13.99 represents 13 whole units and 99 parts of a further unit.
To convert 13.99% to a fraction, remember that percent means "per hundred." Therefore, you first write it as \( \frac{13.99}{100} \). This fraction is not yet free of decimals.
To address this, multiply both the numerator and the denominator by a power of ten that matches the number of decimal places. Here, moving the decimal two places to the right translates into multiplying by 100:

• Numerator: 13.99 becomes 1399 when multiplied by 100.
• Denominator: 100 becomes 10000 when multiplied by 100.

Hence, the conversion gives us \( \frac{1399}{10000} \). This fraction is now expressed without any decimals.

Once a fraction is free of decimals, the next step is simplifying it. Simplifying means reducing it to its smallest form so that it becomes easier to work with or understand. For the fraction \( \frac{1399}{10000} \), simplification involves finding a number that divides both the numerator and the denominator evenly.
A fraction is said to be in its simplest form when no number other than 1 divides both the numerator and the denominator.
If there were a common divisor, you would divide the top and bottom by this number until you can’t anymore. By doing this, the fraction could be broken down into a simpler form that represents the same value.

The greatest common divisor (GCD) plays a crucial role in simplifying fractions. This is the biggest number that can evenly divide both the numerator and the denominator. To find the GCD, list the factors of each number and identify the largest factor they have in common.
In the exercise, we determine that 1399 is a prime number, meaning its only divisors are 1 and 1399 itself. Since 1399 does not divide 10000 evenly, the GCD remains 1, hence the fraction \( \frac{1399}{10000} \) is already in its simplest form.
Understanding how to find the GCD helps in efficiently simplifying fractions, making calculations quicker and easier. Always look for common factors when attempting to simplify fractions, and remember that a prime numerator indicates a simplified state if it does not divide the denominator.