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Chapter 6: Problem 9

Write \(2 \frac{7}{8}\) as a percent. (a) \(2.875 \%\) (b) \(28.75 \%\) (c) \(287.5 \%\) (d) \(2875 \%\)

Short Answer

Expert verified
The answer is (c) 287.5%.

Step by step solution

01

Convert Mixed Number to Improper Fraction

The mixed number given is \(2 \frac{7}{8}\). To convert it to an improper fraction, multiply the whole number 2 by the denominator 8 and then add the numerator 7. This gives us \((2 \times 8) + 7 = 16 + 7 = 23\). Therefore, the improper fraction is \( \frac{23}{8} \).
02

Convert Fraction to Decimal

To convert the fraction \( \frac{23}{8} \) to a decimal, divide 23 by 8. Performing the division, we get \(23 \div 8 = 2.875\). So, \(2 \frac{7}{8}\) is equivalent to the decimal 2.875.
03

Convert Decimal to Percent

To convert the decimal 2.875 to a percent, multiply by 100 and add the percent symbol. This yields \(2.875 \times 100 = 287.5\). Therefore, \(2 \frac{7}{8}\) as a percent is 287.5%, which corresponds to option (c).

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Key Concepts

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

Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It looks like this: \(a \frac{b}{c}\). Here, "\(a\)" is the whole number, and "\(\frac{b}{c}\)" is the fraction.Mixed numbers are useful because they make it easy to communicate values that are more than whole numbers but not complete integers. For example, if you have 2 full apples and 7/8 of another apple, you have \(2 \frac{7}{8}\) apples.When working with mixed numbers, it's often necessary to convert them to improper fractions or decimals. This can simplify mathematical calculations or comparisons.
Improper Fractions
An improper fraction is a fraction where the numerator (the top number) is greater than the denominator (the bottom number). For example, \(\frac{23}{8}\) is an improper fraction because 23 is greater than 8.Improper fractions are useful in mathematical calculations because they represent continuous quantities without breaking them into a separate whole number and fraction. This makes them convenient for operations like addition, subtraction, multiplication, and division.To convert a mixed number into an improper fraction, multiply the whole number by the denominator of the fraction and add the numerator. For \(2 \frac{7}{8}\):
  • Multiply the whole number (2) by the denominator (8): \(2 \times 8 = 16\).
  • Add the numerator (7) to this result: \(16 + 7 = 23\).
  • Place the result over the original denominator: \(\frac{23}{8}\).
Decimals to Percents
Converting decimals to percents is an essential skill in math, as percentages are commonly used to express ratios, proportions, and probabilities. The process is simple:
  • Take the decimal number and multiply it by 100.
  • Add a percent symbol (%) at the end.
For instance, to convert the decimal 2.875 to a percent:
  • Multiply 2.875 by 100, which equals 287.5.
  • Thus, 2.875 as a percent is 287.5%.
Fraction to Decimal Conversion
Converting fractions to decimals involves dividing the numerator by the denominator. This operation turns the fraction into a decimal number, making it easier to interpret and compare with other numbers that are in decimal form.For example, to convert \(\frac{23}{8}\) into a decimal:
  • Divide 23 by 8 using standard division.
  • The result is 2.875, so \(\frac{23}{8} = 2.875\).
Understanding fraction to decimal conversion is crucial in many aspects of math and real-world applications, such as calculating percentages, working with money, and comparing measurements.

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Most popular questions from this chapter

Write \(175 \%\) as a decimal. (a) 0.175 (b) 1.75 (c) 17.5 (d) 1750

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