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Chapter 7: Problem 39

What number is \(54 \frac{1}{3} \%\) of \(6 ?\)

Short Answer

Expert verified
54 1/3% of 6 is approximately 3.26.

Step by step solution

01

Convert the Percentage to a Decimal

To find a percentage of a number, we start by converting the percentage into a decimal. The given percentage is \(54 \frac{1}{3} \%\). First, convert the fraction into a decimal: \(\frac{1}{3} = 0.3333\). So, \(54 \frac{1}{3} \% = 54.3333\%\). Divide by 100 to convert it to a decimal: \(\frac{54.3333}{100} = 0.543333\).
02

Calculate the Percentage of the Number

Now, calculate \(54 \frac{1}{3} \%\) of \(6\) by multiplying the decimal by the number. \(0.543333 \times 6 = 3.26\).
03

Round the Result

The multiplication results in a long decimal number. Usually, we round to the nearest hundredth for a percentage, so the result \(3.26\) is already rounded appropriately.

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Key Concepts

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

Decimal Conversion
Understanding decimal conversion is essential when working with percentage problems. Let's delve into how percentages turn into decimals for easier calculations.

When you have a percentage like 54%, converting it into a decimal helps in mathematical operations. To perform the conversion, you simply divide the percentage by 100:
  • First, write the percentage number over 100. For example, 54% becomes \( \frac{54}{100} \).
  • Then, perform the division to transform it into a decimal: \( 54 \div 100 = 0.54 \).

With percentages that include fractions, such as \(54 \frac{1}{3}\%\), make sure to convert the fraction to a decimal first, then add it to the whole number before dividing by 100. This ensures accuracy in your decimal conversion.
Fraction to Decimal
Converting fractions to decimals is another useful skill, especially when dealing with mixed numbers in percentages. Here's a simple way to manage this conversion:

  • Start with your fraction, for instance, \( \frac{1}{3} \).
  • To convert, divide the numerator by the denominator: \( 1 \div 3 \).
  • The result, in this case, is approximately 0.3333.

Once you have the decimal form of the fraction, add it to any whole number present. In our example, for \(54 \frac{1}{3}\%\), it results in 54.3333%. Breaking down fractions into decimals simplifies subsequent steps, such as finding percentages of other numbers.
Rounding Numbers
Rounding numbers is often the final touch in percentage calculations. It helps present results in a cleaner way. Here鈥檚 a straightforward approach to rounding:

  • Examine the number after your desired decimal place. For instance, in rounding 3.2667 to the nearest hundredth, check the thousandth place.
  • If the digit is 5 or higher, round up, which would change 3.2667 to 3.27.
  • If the digit is less than 5, keep the current hundredth place value, such as 3.26.

This method keeps numbers manageable and easier to interpret in percentage calculations or other mathematical contexts.

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Most popular questions from this chapter

In an election for class president, Raven received \(21 \%\) of the votes, Anita received \(27 \%\), Jamal received \(24 \%\) of the votes, and \(28 \%\) of the votes were received by other candidates. If a pie chart is created for this data, what will be the degree measure of the central angle of the sector representing Raven's share of the vote? Round your answer to the nearest degree.

The balance on a 6-year loan is $$\$ 10,222$$. If the principal borrowed was $$\$ 7,600$$, what was the simple interest rate (as a percent)?

The table shows the number of guard troop services since Sept. 11, 2001 (as of Dec. 2008; some troops have activated multiple times). Associated Press-Times- Standard 02/18/10 Guard troops wait for promised pay. $$ \begin{array}{c|c} \text { Mission } & \text { Troops } \\ \hline \text { Operation Iraqi Freedom } & 193,598 \\ \text { Operation Enduring Freedom } & 29,212 \\ \text { Other missions } & 35,849 \end{array} $$ Use a protractor to help create a pie chart showing the distribution of National Guard troops

A business owner takes out a 2-month loan at a 8.5% per year simple interest rate. At the end of the 2-month loan period, the interest owed is $85. What was the principal amount borrowed?

How much simple interest is earned if $5,800 is invested at 3.25% per year for 4 years?
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