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Chapter 6: Problem 29

Solve. Use the basic percent equation. \(80 \%\) of 16.25 is what?

Short Answer

Expert verified
80% of 16.25 is 13.

Step by step solution

01

Convert percent to decimal

First, convert 80% into a decimal by dividing 80 by 100. This gives \(0.8\).
02

Calculate the part

Next, multiply the converted decimal by the whole number, 16.25. This can be done by multiplying \(0.8\) with \(16.25\). The result is the part you're looking for.

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Key Concepts

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

Basic Percent Equation
The basic percent equation is a fundamental method for finding percentages in math. It's expressed as:
\[\text{Percent} \times \text{Whole} = \text{Part}\]This equation helps you find one component when the other two are known.
For example, if you know 80% of a quantity, you can find "Part" by substituting the percent and whole into the equation.
Using this equation simplifies problem-solving with percentage calculations. It translates percentage expressions into multiplication problems.
Percent to Decimal Conversion
Converting a percent to a decimal is crucial for executing percentage calculations. Remember, "percent" means per hundred.
To convert a percentage:
  • Remove the percent sign
  • Divide the number by 100

For instance, converting 80% to a decimal involves moving the decimal point two places to the left or dividing by 100.
Thus, 80% becomes \(0.8\).
This conversion is essential because it allows you to utilize percentages in equations like multiplying or dividing in calculations.
Multiplying Decimals
Once the percentage is converted to a decimal, the next step is multiplication. Here, we focus on multiplying decimals. It might seem tricky, but it follows basic multiplication rules:
  • Ignore the decimal initially and multiply the numbers as usual.
  • Count the total number of decimal places in both numbers.
  • In your answer, ensure it contains the same number of decimal places counted.

For our example, multiply \(0.8\) with \(16.25\). You perform the multiplication and then, ensure that your answer correctly reflects the decimal places adjusted.
Understanding this concept ensures you accurately calculate the "Part" of the equation.
Problem Solving Steps
Solving percentage problems systematically ensures accuracy and clarity. Follow these steps:
  • **Identify the problem components:** Recognize the whole, percent, and the part you need to find.
  • **Convert the percentage:** Use the percent to decimal conversion technique to prepare the percentage for calculations.
  • **Apply the equation:** Insert the known values into the basic percent equation.
  • **Calculate:** Multiply the decimal with the whole.
    Ensure that you follow all arithmetic rules.

This structured approach guarantees that each step builds on the previous one, leading you to the correct answer without confusion.

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Most popular questions from this chapter

Write as a decimal. $$18.23 \%$$

For \(0.75 \%,\) the percent ratio is the ratio \(\frac{0.75}{100} .\) Which of the following fractions are equivalent to this ratio? (i) \(\frac{3}{4}\) (ii) \(\frac{3}{400}\) (iii) \(\frac{75}{10,000}\)

Write the comparison as a ratio in simplest form using a fraction, a colon (:), and the word \(t o\). 8 days to 12 days

The American Red Cross spent \(\$ 185,048,179\) for administrative expenses. This amount was \(3.16 \%\) of its total revenue. Find the American Red Cross's total revenue. Round to the nearest hundred million.

Write as a percent. $$1.36$$
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