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Chapter 7: Problem 23

What number is 18.4% of 125?

Short Answer

Expert verified
18.4% of 125 is 23.

Step by step solution

01

Convert Percentage to Decimal

To find a percentage of a number, you first convert the percentage into a decimal by dividing by 100. So, for 18.4%, the decimal form is \( \frac{18.4}{100} = 0.184 \).
02

Multiply by the Total

Next, multiply the decimal by the total number to find the part that is the percentage of the total. Multiply 0.184 by 125: \[ 0.184 \times 125 = 23 \]
03

Verify the Calculation

As a final step, double-check the multiplication to ensure there are no errors. Recompute:\[ 0.184 \times 125 = 23 \] confirming the calculation.

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Key Concepts

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

Decimal Conversion
To understand percentages better, it helps to know how to convert them into decimal form. Percentages show how much of something there is out of 100 parts. When you want to perform calculations, it鈥檚 often easier to use decimals rather than percentages.

The process of converting a percentage to a decimal is simple:
  • Divide the percentage by 100.
  • This will shift the decimal point two places to the left.
  • For example, converting 18.4% into a decimal would involve the calculation: \( \frac{18.4}{100} = 0.184 \).
The resulting decimal, 0.184, is a more convenient way to work with percentages for further calculations. You use this decimal in multiplication to find specific values, like how much is 18.4% of 125.
Multiplication
Once the percentage is converted into a decimal, finding a portion of a whole number becomes straightforward. You will use multiplication to figure out this value.

Here's how you multiply the decimal by the total:
  • Take the decimal form of the percentage, *e.g.,* 0.184, that you calculated in the first step.
  • Multiply this number by the whole quantity you are interested in, *e.g.,* 125.
  • The multiplication looks like this: \( 0.184 \times 125 \).
The result of multiplying 0.184 by 125 gives you 23, meaning 18.4% of 125 is 23. This multiplication is crucial as it helps you to determine precisely what fraction of the whole number your percentage represents.
Verification of Calculations
Verifying calculations is an essential step to ensure that you haven鈥檛 made any mistakes. It's always a good idea to double-check your multiplication results, especially when working with percentages and decimals.

Here's how you can verify your calculation:
  • Repeat the multiplication process to see if the results match.
  • You can also use a calculator to double-check complex calculations.
  • Consider breaking down calculations to smaller steps if necessary to understand each part.
In our example, recomputing \( 0.184 \times 125 \) resulted again in 23, confirming the accuracy of our result. This thorough verification ensures confidence in your solution and is good practice in any mathematical problem-solving scenario.

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Most popular questions from this chapter

A business owner borrows $$\$ 4,000$$ for 3 months. At the end of the 3-month loan period, the interest owed is $$\$ 35$$. What was the simple yearly interest rate (as a percent)?

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.

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In an election for class president, the vote distribution among three candidates is shown in the following table. $$ \begin{array}{c|c} \text { Candidate } & \text { Votes } \\ \hline \text { Raven } & 43 \\ \text { Mabel } & 40 \\ \text { Bernardo } & 52 \\ \hline \end{array} $$ Use a protractor to help create a pie chart showing the distribution of votes.

A business owner borrows $$\$ 7,300$$ for 2 months. At the end of the 2-month loan period, the interest owed is $$\$ 73$$. What was the simple yearly interest rate (as a percent)?
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