Problem 10 - Elementary Algebra

Question

For the following problems, convert each fraction to a percent. $$ \frac{7}{27} $$

Step-by-Step Solution

Answer

Answer: The fraction 7/27 is approximately equal to 25.9%.

Step 1: Convert Fraction to Decimal

To convert the fraction \(\frac{7}{27}\) to a decimal, divide the numerator (7) by the denominator (27). This can be written as: $$ \frac{7}{27} = 7 \div 27 $$ Perform the division to obtain the decimal: $$ 7 \div 27 \approx 0.259 $$ So, \(\frac{7}{27}\) is approximately equal to \(0.259\) as a decimal.

Step 2: Convert Decimal to Percent

Now, we will convert the decimal 0.259 to a percent. To do this, multiply the decimal by 100 and add the percent sign (%): $$ 0.259 \times 100 = 25.9\% $$ Thus, the fraction \(\frac{7}{27}\) is approximately equal to \(25.9\%\).

Key Concepts

Understanding Fractions

Fractions are a way of expressing numbers that are not whole. They provide a way to represent any number between whole numbers, and they consist of a numerator and a denominator. The numerator is the top number, showing how many parts of the whole we have. The denominator is the bottom number, showing the total number of equal parts the whole is divided into.
For example, in the fraction \( \frac{7}{27} \), 7 is the numerator and 27 is the denominator. This fraction tells us that we have 7 parts of a whole that is divided into 27 equal parts.

• The larger the denominator, the smaller each part is.
• If the numerator is equal to the denominator, the fraction is equal to 1, or a whole.
• If the numerator is less than the denominator, the fraction is less than 1.

Converting Fractions to Decimals

To convert a fraction into a decimal, we simply divide the numerator by the denominator. This division gives us a decimal equivalent of the fraction, which is often easier to interpret in situations involving money, measurements, or percentages.
For our example, let's convert \( \frac{7}{27} \) to a decimal. We perform the division: \( 7 \div 27 \), which approximately equals 0.259. Here are the steps for conversion:

• Take the numerator (7) and divide it by the denominator (27).
• Perform the division using long division or a calculator.
• The result is a decimal number, approximately 0.259 in this case.

Using a calculator can make this process quicker and more accurate, especially for fractions with large numbers.

Understanding and Converting to Percentages

Percentages are a way of expressing numbers as parts of 100. They are commonly used to describe proportions, such as discounts or grades. To convert a decimal into a percentage, we simply multiply the decimal by 100. This shifts the decimal point two places to the right and adds a percent sign (%).
In our earlier example, we converted \( 0.259 \) to a percentage by multiplying it by 100, resulting in 25.9%. Here are the steps:

• Take the decimal form of the number, like 0.259.
• Multiply the decimal by 100.
• Add the percent sign to the result.
• So, \( 0.259 \times 100 = 25.9\% \).

This method of converting decimals to percentages is very useful when you want to understand how a part of anything compares to the whole, expressed as a fraction of 100.