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Chapter 7: Problem 71

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{5}{11}$$

Short Answer

Expert verified
45.5%

Step by step solution

01

- Convert the Fraction to a Decimal

To convert the fraction \(\frac{5}{11}\) to a decimal, divide 5 by 11. \(\frac{5}{11} 鈮� 0.4545454545\).
02

- Convert the Decimal to Percent

Multiply the decimal by 100 to change it to percent notation: \(0.4545454545 \times 100 = 45.45454545\).
03

- Round to the Nearest Tenth

Round the result to the nearest tenth of a percent: \(45.45454545\) rounds to 45.5%.

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Key Concepts

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

Fraction to Decimal Conversion
The first step in converting a fraction to a percent is to turn the fraction into a decimal. This process involves dividing the numerator (top number) by the denominator (bottom number). For example, if you have the fraction \( \frac{5}{11} \), you would divide 5 by 11. Doing the division, you will get a repeating decimal: \( 0.4545454545 \.\.\. \). Understanding the relationship between fractions and decimals is crucial for this step. Each fraction has a corresponding decimal that either terminates or repeats. To proceed, we use this decimal value for the next steps.
Decimal to Percent Conversion
Once you have your decimal, the next step is converting it to a percent. Percent means per hundred, so you multiply the decimal by 100. Using our decimal from the previous step, \( 0.4545454545 \), multiply it by 100 to move the decimal point two places to the right. This gives us \( 45.45454545 \). The multiplication can be remembered as a simple movement of the decimal point because percent literally breaks down to 'per cent' or 'per hundred'. This transformation helps in understanding percentages as more user-friendly and relatable figures.
Rounding Decimals
Finally, after converting the decimal to a percent, we often need to round it to a certain precision. In our example, we need to round to the nearest tenth of a percent. The percent we got is \( 45.45454545 \). To round it, look at the hundredths place (second digit after the decimal point). If it's 5 or more, round up the tenths place by one, if less, leave the tenths place as it is. Here, the hundredths digit is 4, so \( 45.45 \) remains \( 45.5 \) rounded to the nearest tenth. This step makes the percentage more readable and practical for most uses. Rounding is a useful skill in many mathematical and real-world applications, making numbers easier to work with and understand.

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Most popular questions from this chapter

Solve the problem using a percent equation. What is \(45 \%\) of \(62 ?\)

Solve the problem using a percent equation. 1.2 is what percent of \(600 ?\)

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{8}{11}$$

It is customary to leave a \(15-20 \%\) tip for the server in a restaurant. However, when you are at a restaurant in a social setting, you probably do not want to take out a pencil and piece of paper to figure out the tip. It is more socially acceptable to compute the tip mentally. Try this method. Step 1: First, if the bill is not a whole dollar amount, simplify the calculations by rounding the bill to the next-higher whole dollar. Step 2: Take \(10 \%\) of the bill. This is the same as taking one-tenth of the bill. Move the decimal point to the left 1 place. Step 3: If you want to leave a 20\% tip, double the value found in step 2. Step 4: If you want to leave a \(15 \%\) tip, first note that \(15 \%\) is \(5 \%+10 \% .\) Therefore, add one-half of the value found in step 2 to the number in step 2 . Estimate a \(15 \%\) tip on a luncheon bill of \(\$ 12.00\)

Convert the fraction to a percent. $$\frac{71}{100}$$
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