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Chapter 7: Problem 71

Convert \(15 / 7\) to a percent, and round your answer to the nearest tenth of a percent.

Short Answer

Expert verified
214.3%

Step by step solution

01

Divide the Fraction

Convert the fraction \(\frac{15}{7}\) to a decimal by performing the division: \(15 \div 7\). This results in approximately 2.142857.
02

Convert to a Percentage

Multiply the decimal result by 100 to convert it to a percentage: \(2.142857 \times 100 = 214.2857\).
03

Round to Nearest Tenth

Round the percentage to the nearest tenth. The number 214.2857 rounded to the nearest tenth is 214.3.

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Key Concepts

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

Fraction to Decimal Conversion
To convert a fraction to a decimal, the process is straightforward: simply divide the numerator by the denominator. In the case of the fraction \( \frac{15}{7} \), divide 15 by 7. This will give you the decimal value. Performing this division results in \( 2.142857 \).
This decimal is a repeating decimal, which means the pattern "142857" will continue indefinitely.

Here's a quick reminder of how you handle division:
  • Set up the division problem as a long division if necessary.
  • Divide the numerator (15) by the denominator (7).
  • If needed, add zeros to the right of the decimal point and continue dividing until you see the decimal repeating or reach a satisfactory level of precision.
Understanding this conversion is crucial as it forms a foundation for the next steps in converting to percentages.
Decimal to Percent Conversion
Converting a decimal to a percentage involves a simple multiplication.
You take the decimal, in this case, \( 2.142857 \), and multiply it by 100. This is because a percentage is essentially a fraction out of 100.

The calculation looks like this:
  • Decimal: \( 2.142857 \)
  • Formula: Decimal \( \times \) 100
  • Calculation: \( 2.142857 \times 100 = 214.2857 \)
This step increases the scale of the number, turning the decimal into a recognizable percentage.
Always remember that multiplying by 100 moves the decimal point two places to the right.
Rounding Decimals
Rounding decimals is an important skill, especially when you want clarity in your results or when your calculations result in a long string of numbers.
When instructed to round to the nearest tenth, focus on the first decimal place after the point. Here, take \( 214.2857 \). Observe the number in the second decimal place (8 in this case).

To round:
  • If this digit is 5 or greater, increase the first decimal place by 1.
  • If it is less than 5, keep the first decimal place unchanged.
Applying this to our example, the number "8" is greater than 5, so you increase the "2" in the tenths place to "3".
This results in the decimal rounding to \( 214.3 \).
Rounding makes the number easier to work with and understand, especially in contexts like percentage calculations where precision to tenths can be sufficient.

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