- Convert percentages to their fractional form by placing the number over 100.
- Divide the numerator by the denominator to convert to a decimal: \(25\% = \frac{25}{100} = 0.25\).
- Simplify fractions if possible: \(9\% = \frac{9}{100}\), which is already in simplest form.
- Final Answers: \(25\% = \boxed{0.25}\) and \(9\% = \boxed{\frac{9}{100}}\).
Explanation
- Analyzing the Problem and Definitions
The problem asks us to convert two given percentage values into different formats. A percentage, denoted by the symbol \(\%\), represents a portion of 100. By definition, a value \(x\%\) is equivalent to the fraction \(\frac{x}{100}\).
To convert a percentage into a decimal, we perform the division by 100. For instance, if we have \(25\%\), we interpret this as \(\frac{25}{100}\). Performing this division gives us \(0.25\).
To convert a percentage into a fraction, we write it as a fraction with a denominator of 100 and then simplify the fraction if the numerator and denominator share any common factors other than 1. For the value \(9\%\), we write it as \(\frac{9}{100}\). We then examine if 9 and 100 have any common factors. Since 9 is only divisible by 1, 3, and 9, and none of these divide 100, the fraction is already in its simplest form.
- Performing the Conversions
First, we convert 25% to a decimal. Following the definition, we have:
\[25\% = \frac{25}{100} = 0.25\]
Second, we convert 9% to a fraction. Following the definition, we have:
\[9\% = \frac{9}{100}\]
As determined previously, this fraction cannot be simplified further because the greatest common divisor of 9 and 100 is 1. Thus, the conversions are \(0.25\) and \(\frac{9}{100}\), respectively.
Examples
Percentages are widely used in daily life to understand proportions and make financial decisions. For example, if a store offers a 25% discount on an item originally priced at \(\$100\), you can quickly calculate the savings as \(\$100 \times 0.25 = \$25\). Similarly, if you want to determine the probability of an event occurring and you find it is 9%, expressing this as a fraction \(\frac{9}{100}\) helps you understand the likelihood in terms of "9 chances out of 100." Understanding how to switch between percentages, decimals, and fractions is a fundamental skill for interpreting data and managing money effectively.