Problem 7 - Elementary Algebra

Question

For the following problems, convert each fraction to a percent. $$ \frac{2}{9} $$

Step-by-Step Solution

Answer

Question: Convert the fraction $$\frac{2}{9}$$ into a percentage using the step-by-step solution provided. Answer: The fraction $$\frac{2}{9}$$ converted into a percentage is approximately 22.22%.

Step 1: Understand the conversion

To convert a fraction into a percentage, you will need to divide the numerator by the denominator and then multiply the result with 100.

Step 2: Divide the numerator by the denominator

Divide the numerator of the given fraction, 2, by the denominator, 9. $$ \frac{2}{9} = 0.2222... $$

Step 3: Multiply the result by 100

Now, multiply the result from Step 2 by 100 to convert the decimal to a percentage. $$ 0.2222... \times 100 = 22.22... $$

Step 4: Round the result (Optional)

If required by the exercise, you can round the result to a desired number of decimal places. In this case, let's round to two decimal places: $$ 22.22 $$

Step 5: Write the answer in percentage

In the final step, write the answer with the percentage symbol: $$ 22.22\% $$ So, the fraction $$\frac{2}{9}$$ converted to a percentage is approximately 22.22%.

Key Concepts

Fraction to Percent Conversion

Understanding how to convert fractions to percentages is an essential mathematical skill that finds application in everyday life, such as calculating discounts, interpreting statistics, or analyzing data. To perform a fraction to percent conversion, you need to comprehend that a percentage is simply a fraction with a denominator of 100. Here’s a straightforward approach to turning any fraction into a percent:

First, divide the fraction's numerator (the top number) by the denominator (the bottom number). This division will give you a decimal. Using the example from the exercise, when you divide 2 by 9, you get approximately 0.2222. Next, multiply this decimal by 100 to shift the decimal point two places to the right. This multiplication translates your decimal into a percent. In our example, 0.2222 multiplied by 100 equals 22.22 percent. Remember, moving the decimal point to the right twice is the same as multiplying by 100. This simple method unlocks the power to seamlessly transition between fractions and percentages.

Decimal to Percentage

While working with numbers, it’s often necessary to switch from a decimal form to a percentage. Decimal to percentage conversion is a basic yet vital concept and it’s very simple to grasp. To convert a decimal to a percentage, multiply it by 100. This moves the decimal point two places to the right, effectively transforming the number into a percent based on the understanding that 'percent' means 'per hundred'.

For instance, imagine you have a decimal like 0.75. When we convert this to a percentage, it becomes 0.75 times 100, which is 75%. This is crucial to realize that you're not changing the value of the number, but rather expressing the same value in a different form. Multiplying by 100 is the same as saying the decimal 'out of 100', which is precisely what a percentage represents. It’s a helpful way to communicate fractions in a format that is often easier for people to understand.

Rounding Percentages

When presenting data, especially in percentages, it's sometimes important to round the percentages to make them more digestible and user-friendly. Rounding percentages can also be a matter of significant figures or desired precision. This means you might not always want to express your percentage down to the smallest fraction of a percent. Take the earlier exercise as an example; the exact decimal we got was 0.2222, which turned into a percentage of 22.22...%

Typically, you would round this to a fixed number of decimal places, most commonly two, unless otherwise specified. In our case, rounding to two decimal places, you get approximately 22.22%. Remember, when the digits following the decimal are 5 or more, you round up the last kept digit. If they are 4 or less, you keep the last digit as is. This rounding provides us with a cleaner, more approachable number for reporting, discussions, and application.