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Chapter 7: Problem 62

Convert the fraction to a percent. $$2 \frac{1}{8}$$

Short Answer

Expert verified
212.5%

Step by step solution

01

Convert Mixed Number to Improper Fraction

To convert the mixed number \(2 \frac{1}{8}\), multiply the whole number part by the denominator and then add the numerator. \[ 2 \frac{1}{8} = \frac{2 \times 8 + 1}{8} = \frac{16 + 1}{8} = \frac{17}{8} \]
02

Divide the Numerator by the Denominator

To convert the improper fraction \(\frac{17}{8}\) to a decimal, divide the numerator by the denominator. \[ \frac{17}{8} = 2.125 \]
03

Convert the Decimal to a Percent

Multiply the decimal value by 100 to convert it to a percent. \[ 2.125 \times 100 = 212.5 \] Thus, the fraction \(2 \frac{1}{8}\) as a percent is 212.5%.

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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 proper fraction. For example, in the mixed number \(2 \frac{1}{8}\), 2 is the whole number, and \( \frac{1}{8} \) is the proper fraction. Mixed numbers are useful when representing quantities that are more than one whole but less than the next whole number.
To work with mixed numbers in calculations, we often convert them into improper fractions. This makes mathematical operations easier to perform.
improper fractions
Improper fractions have a numerator that is greater than or equal to the denominator. For instance, \( \frac{17}{8} \) is an improper fraction because 17 is larger than 8.
Converting a mixed number to an improper fraction involves a few simple steps:
  • Multiply the whole number by the denominator of the fraction
  • Add the numerator to this result
  • Write the sum over the original denominator
Using our example, \( 2 \frac{1}{8} = \frac{17}{8} \). This process makes it easier to convert fractions into decimals and percentages later.
decimal conversion
Decimal conversion is the process of transforming fractions into their decimal form. To convert an improper fraction like \( \frac{17}{8} \) into a decimal, divide the numerator (17) by the denominator (8). The calculation will be: \( 17 梅 8 = 2.125 \).
This results in the decimal form of the fraction. Decimal numbers are easier to manipulate in many mathematical contexts, such as addition, subtraction, multiplication, and division.
percentages
Percentages are a way to express a number as a fraction of 100. To convert a decimal into a percentage, multiply the decimal by 100. For instance, \(2.125 \times 100 = 212.5\).
Hence, the decimal 2.125 corresponds to 212.5%. Understanding how to move between fractions, decimals, and percentages is essential for solving many real-world problems.
  • This includes scenarios like calculating discounts, determining interest rates, and interpreting data in statistics.

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Most popular questions from this chapter

Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 14,000$$ Annual Interest Rate $$4.5 \%$$ Time, Years $$3$$ Compounded Monthly Total Amount __________

Find the total amount in an account for an investment subject to the following conditions. Principal $$\$ 10,000$$ Annual Interest Rate $$6 \%$$ Time, Years $$1 \frac{1}{2}$$ Compounded Quarterly Total Amount __________

Find the decimal and fraction equivalents of the percent given in the sentence. During a period of a weak economy and rising fuel prices, low-fare airline, Southwest, raised its average fare during the second quarter by \(8.4 \%\) (Source: USA TODAY)

Convert the decimal to a percent. $$1.75$$

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