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Chapter 8: Problem 26

Write each fraction as a percent. $$\frac{3}{4}$$

Short Answer

Expert verified
Answer: The equivalent percentage of the fraction $$\frac{3}{4}$$ is $$75\%$$.

Step by step solution

01

Convert the fraction to a decimal

Divide the numerator by the denominator to convert it into a decimal: $$\frac{3}{4} = 0.75$$
02

Convert the decimal to a percent

Multiply the decimal by 100 to get the percentage: $$0.75 \times 100 = 75$$
03

Add the percent sign

Include the percent sign to the answer: $$75\%$$ The fraction $$\frac{3}{4}$$ is equal to $$75\%$$.

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Key Concepts

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

Decimal Conversion
Converting a fraction into a decimal is a straightforward process. The key is to understand that a fraction is essentially a division of two numbers. These numbers are known as the numerator and the denominator. For example, in the fraction \( \frac{3}{4} \), 3 is the numerator, and 4 is the denominator. To convert this fraction into a decimal, you divide the numerator (3) by the denominator (4). When you perform this division, you'll find that \( 3 \div 4 = 0.75 \). Now, you have successfully converted the fraction \( \frac{3}{4} \) into the decimal 0.75.

There are some tips to make this easier:
  • Always ensure your division setup is correct, numerator divided by the denominator.
  • If your division doesn鈥檛 end, you may have a repeating decimal. Use a calculator for efficiency.
Percentage Calculation
Once a fraction is expressed as a decimal, the next step involves converting this decimal into a percentage. Percent means per hundred, so moving from decimals to percentages involves comparing the decimal to 100. The straightforward method is multiplying the decimal by 100.

Let鈥檚 continue with our example: we have the decimal 0.75. To convert that into a percentage, multiply 0.75 by 100 and you get 75. Thus, \( 0.75 \times 100 = 75 \). Now, our decimal has transformed into a nice round number signifying a percentage value.

Using this method:
  • Multiplying by 100 effectively shifts the decimal point two places to the right.
  • This operation is consistent for any decimal you wish to convert to a percentage.
Percent Sign
Adding the percent sign is a crucial final touch in expressing values as percentages. It's a small symbol, but it holds significant meaning, indicating that the number is a percentage. When representing a number as a percentage, the percent sign (%) is always placed immediately after the number.

Continuing from our example, after calculating that 0.75 turns into 75 through multiplication, the last step is to attach a percent sign. Hence, the final representation is 75%, which tells us that we're dealing with a percentage of a whole.

Key things to remember about the percent sign:
  • It helps to communicate clearly that the number is a percentage, not a decimal or another format.
  • In mathematical information and real-world data, percentages offer a familiar way to express ratios and comparisons.

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Most popular questions from this chapter

Translate to an equation and solve. Wright earns \(10 \%\) of total sales in commission. If he sells \(\$ 3106\) in merchandise over a two-week period, what is his commission?

In one season, a football kicker scores 33 extra points in 35 attempts. What percent of his attempts did he score?

Write each decimal number as a percent. $$0.8$$

Draw a circle graph showing each percent. Students in an English course can earn an \(\mathrm{A}, \mathrm{a} \mathrm{B}, \mathrm{a} \mathrm{C}\) or an F. The following table shows the results of a class. $$\begin{array}{c|c} \mathrm{A} & 12 \% \\ \hline \mathrm{B} & 25 \% \\ \hline \mathrm{C} & 45 \% \\ \hline \mathrm{F} & 18 \% \end{array}$$ (GRAPH CANT COPY)

Solve. Vladimir purchased a set of golf clubs discounted \(15 \%\). If the price after the discount was \(\$ 577.96\), what was the initial price?
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