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Chapter 7: Problem 67

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{3}{7}$$

Short Answer

Expert verified
42.9%

Step by step solution

01

Convert the Fraction to a Decimal

To convert \(\frac{3}{7}\) into a decimal, divide the numerator (3) by the denominator (7). \(\frac{3}{7} 鈮� 0.428571\)
02

Multiply by 100 to Get a Percentage

Once the decimal is calculated (0.428571), multiply it by 100 to convert it into a percentage. \(0.428571 \times 100 = 42.8571\)
03

Round to the Nearest Tenth

Round the percentage to the nearest tenth. 42.8571 rounded to the nearest tenth is 42.9.

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Key Concepts

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

Percent Notation
Understanding percent notation is crucial. A percent represents a part out of 100. For example, 50% means 50 out of every 100. To write any number as a percent, you multiply it by 100 and then add the percent symbol (%).
In our exercise, converting \(\frac{3}{7}\) to a percent involves two main steps: converting the fraction to a decimal and then converting the decimal to a percent. We'll explore these steps more in our next sections.
Decimal Conversion
To convert a fraction to a decimal, divide the numerator (the top number) by the denominator (the bottom number).
In our example, \(\frac{3}{7}\) means dividing 3 by 7, which gives approximately 0.428571.
Decimal conversion is the foundation for percent notation. Always ensure to perform the division accurately. Here are some tips:
  • Use a calculator for precision.
  • Understand that some fractions may result in repeating (non-terminating) decimals.
With our fraction \(\frac{3}{7}\), 0.428571 is the repeating decimal value that we'll use to find the percentage.
Rounding Percentages
Rounding is important for simplifying percentages. Once you've converted a fraction to a decimal and then to a percentage, you may need to round it to make it easier to understand.
To round to the nearest tenth of a percent, look at the number in the hundredths place. If it's 5 or more, round up. If it's less than 5, round down.
For our example, 42.8571% rounds to 42.9% because the hundredths place (5) is 5 or greater.
Here are some rounding tips:
  • Always start at the digit you need to round to.
  • Check the digit immediately after it.
  • Apply the rounding rule (5 or more, go up; less than 5, go down).
This makes the final result more presentable and easier to communicate.

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Most popular questions from this chapter

Yellowstone National Park has \(3366 \mathrm{mi}^{2}\) of undeveloped land. If this represents \(99 \%\) of the total area, find the total area of the park.

Explain the difference between \(25 \%\) and \(0.25 \%\)

Convert the fraction to a percent. $$\frac{89}{100}$$

If a bank compounds interest monthly for 2 years, how many total compounding periods are there?

Solve the problem using a percent equation. \(12 \%\) of what number is \(26.4 ?\)
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