Problem 71 Write the fraction in percent no... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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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

- Convert the Fraction to a Decimal

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

- Convert the Decimal to Percent

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

- 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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91影视

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

Short Answer

Step by step solution

- Convert the Fraction to a Decimal

- Convert the Decimal to Percent

- Round to the Nearest Tenth

Key Concepts

Fraction to Decimal Conversion

Decimal to Percent Conversion

Rounding Decimals

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