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Chapter 7: Problem 74

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{1}{15}$$

Short Answer

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Step by step solution

01

Convert the fraction to a decimal

Divide the numerator by the denominator: \( \frac{1}{15} \). Performing the division, we get: \( \frac{1}{15} = 0.0667 \). Note that the decimal is approximately 0.0667 (rounded to four decimal places).
02

Convert the decimal to a percentage

To convert a decimal to a percentage, multiply by 100. So, \( 0.0667 \times 100 = 6.67 \).
03

Round to the nearest tenth

The value 6.67 is already rounded to the nearest tenth. Therefore, the percentage is 6.7%.

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Key Concepts

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

Fraction to Decimal
When we convert a fraction to a decimal, we are essentially dividing the numerator (the top number) by the denominator (the bottom number). For example, with the fraction \(\frac{1}{15}\), we divide 1 by 15.
Performing the division using a calculator or long division, we get:
\[ \frac{1}{15} = 0.0667 \](approximately to four decimal places).
This step is crucial because decimals are often easier to work with than fractions.
Percent Notation
Percent notation expresses a number as a part of 100. To convert a decimal to a percentage, simply multiply it by 100. Let's take our decimal from the previous step:
\(0.0667 \times 100 = 6.67\).
This tells us that the fraction \(\frac{1}{15}\) is equivalent to 6.67% when represented as a percentage. This step allows for easier comparison and understanding of values.
Rounding Decimals
Rounding decimals is the process of reducing the number of digits right of the decimal point while keeping the value close to what it originally was. In our example, we have the percentage 6.67%:
  • To round to the nearest tenth, look at the hundredths place (the digit right after the tenths place).
  • If this digit is 5 or higher, round up the tenths place by one.
  • If it is less than 5, keep the tenths place as it is.
In 6.67%, the hundredths place is 7 (which is more than 5). So, we round up the tenths place to get:
6.7%. This is our final value rounded to the nearest tenth of a percent.

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