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Chapter 6: Problem 357

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

Short Answer

Expert verified
22.2\text{ (repeating)}\text{%}

Step by step solution

01

Understand the Fraction

The fraction given is \(\frac{2}{9}\). This needs to be converted to a percent.
02

Divide the Numerator by the Denominator

To convert a fraction to a decimal, divide the numerator (2) by the denominator (9): \(\frac{2}{9} 鈮� 0.222\text{ (repeating)}\).
03

Convert Decimal to Percent

To convert the decimal to a percent, multiply by 100: \(0.222 \times 100 鈮� 22.2\text{ (repeating)}\).
04

Final Answer

Thus, \(\frac{2}{9}\) as a percent is approximately \(22.2\text{ (repeating)}\text{%}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

fraction to decimal conversion
Understanding how to convert a fraction to a decimal is vital. Let's break it down with \(\frac{2}{9}\) as an example. We need to divide the numerator (the top number) by the denominator (the bottom number). In this case, divide 2 by 9. It doesn鈥檛 divide evenly, so we get a decimal value. The division results in approximately 0.222, where the digit 2 repeats indefinitely. This repeating sequence is why we write it as 0.222... This is all there is to converting a fraction to a decimal. Always remember to divide the top number by the bottom number.
decimal to percent conversion
After converting a fraction to a decimal, the next step is to turn the decimal into a percent. This step is simpler. First, take our result from before: 0.222. To convert this decimal into a percent, multiply it by 100. When we do this, we move the decimal point two places to the right. Hence, 0.222 becomes 22.2. Always multiply the decimal by 100 to find the percent. This is true for any decimal, not just repeating ones.
repeating decimals
Repeating decimals can be tricky, but they follow a consistent pattern. With our example of \(\frac{2}{9}\), the division results in 0.222..., where the 2 is repeating. To indicate a repeating decimal, we often place a bar above the repeating digit (or digits). For instance, \(\frac{2}{9}\ \approx 0.\bar{2}\). This tells us that the 2 continues infinitely. In calculations, recognizing repeating decimals helps ensure accuracy, particularly when converting them to percentages or performing other mathematical operations.

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Most popular questions from this chapter

In the following exercises, solve. One granola bar has 2 grams of fiber, which is 8\(\%\) of the recommended daily amount. What is the total recommended daily amount of fiber?

Solve the applications of percents. A grilled chicken salad at a popular fast food restaurant contains 650 milligrams (mg) of sodium, which is 27% of the recommended daily amount. What is the total recommended daily amount of sodium?

In the following exercises, convert each percent to (a) a decimal (b) a simplified fraction. $$ 5 \% $$

Solve the applications of percents. One serving of trail mix has 67 grams of carbohydrates, which is 22% of the recommended daily amount. What is the total recommended daily amount of carbohydrates?

In the following exercises, solve the percent problem. The total number of vehicles on one freeway dropped from \(84,000\) to \(74,000\) . Find the percent decrease (round to the nearest tenth of a percent).
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