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Chapter 7: Problem 53

Convert the given fraction to a percent. $$ \frac{5}{2} $$

Short Answer

Expert verified
The fraction \( \frac{5}{2} \) is 250\%.

Step by step solution

01

Understand the Given Fraction

The fraction given in the problem is \( \frac{5}{2} \). This represents the division of 5 by 2.
02

Convert the Fraction to a Decimal

To convert the fraction to a decimal, divide the numerator by the denominator: \( 5 \div 2 = 2.5 \). Therefore, \( \frac{5}{2} = 2.5 \).
03

Convert the Decimal to a Percent

To change a decimal to a percent, multiply the decimal by 100. For the decimal \( 2.5 \), calculate \( 2.5 \times 100 = 250 \). Hence, \( 2.5 \) converts to \( 250\% \).

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Key Concepts

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

Fraction to Decimal Conversion
When faced with a fraction like \( \frac{5}{2} \), the first step towards conversion is translating this into a decimal. A fraction represents a division problem, where the numerator (top number) is divided by the denominator (bottom number). In this case, dividing 5 by 2 yields the decimal 2.5. Converting fractions to decimals simplifies comparisons with other numbers, aiding in further calculations. Decimals are often seen as more intuitive, especially when dealing with everyday situations involving money, measurements, or quantities.
Division in Mathematics
Division is one of the fundamental mathematical operations alongside addition, subtraction, and multiplication. It involves determining how many times a number, the dividend, can be evenly split by another number, the divisor. Here, with \( \frac{5}{2} \), you determine how many times 2 fits into 5. This process is crucial in breaking down complex numbers into simpler forms, like decimals. Understanding division aids in handling various numerical tasks and can clear up confusion when simplifying fractions, solving algebraic equations, or dealing with proportions.
Decimal to Percent Conversion
Once you have a decimal like 2.5, converting it into a percentage helps express the number in a different, often more meaningful way. To perform this conversion, multiply the decimal by 100. This shifts the decimal point two places to the right, transforming 2.5 into 250%. Using percentages is valuable because it helps communicate the size of a number relative to 100, making it easier to understand increases, decreases, and proportions. It's a useful tool in many real-world applications, from analyzing data to gauging interest rates or assessing financial growth.

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Most popular questions from this chapter

Suppose that $5,200 is invested at 3.5% simple interest per year. What will the balance be after 2 years?

Suppose that $8,100 is invested at 8.25% simple interest per year. What will the balance be after 4 years?

The balance on a 8-year loan is $3,160. If the simple interest rate is 7.25% per year, what was the principal borrowed?

In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Mercy } & 56 \\ \text { Hans } & 53 \\ \text { Lisa } & 41 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

A car rack marked at $$\$ 358$$ is sold for $$\$ 292$$. Find the percent discount, correct to the nearest tenth of a percent.
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