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Chapter 4: Problem 12

Find each result using any method you like. \(19 \%\) of 43

Short Answer

Expert verified
19% of 43 is 8.17.

Step by step solution

01

- Convert Percentage to Decimal

To find 19% of 43, first convert the percentage to a decimal. This is done by dividing 19 by 100. \[ 19 \text{ %} = \frac{19}{100} = 0.19 \]
02

- Multiply the Decimal with the Number

Next, multiply the decimal obtained in Step 1 by 43. This gives the following result: \[ 0.19 \times 43 = 8.17 \]
03

- Conclude the Result

The product gives us the final result. Hence, 19% of 43 is 8.17.

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Key Concepts

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

Converting Percentages to Decimals
When working with percentages, converting them into decimals makes calculations easier. To convert a percentage to a decimal, simply divide by 100. For example, to convert 19% to a decimal, you divide 19 by 100. This gives us the decimal form 0.19.

Here is the formula for converting percentages to decimals: \[ \text{Decimal} = \frac{\text{Percentage}}{100} \] This step is crucial and makes the next part of the calculation straightforward. By converting percentages into simpler decimal form, you can more easily multiply them with other numbers.
Multiplication
Once you've converted the percentage into a decimal, the next step is to multiply it by the number in question. This step involves simple multiplication.

For example, after converting 19% to 0.19, you multiply 0.19 by 43. This can be written as: \[ 0.19 \times 43 = 8.17 \] Multiplying decimals follows the same principles as whole numbers, but you must keep track of the decimal points. The product in this case, 8.17, represents the value of 19% of 43.
  • Step 1: Align the numbers by their decimal points.
  • Step 2: Multiply as you would whole numbers.
  • Step 3: Count the total number of decimal places in the multiplicands.
  • Step 4: Place the decimal point in the product, counting from the right.
Step-by-Step Problem Solving
Solving percentage problems in a step-by-step manner helps in organizing your work and avoiding errors. Here's a clear method:

  1. **Step 1:** Convert the percentage to a decimal. In our example, convert 19% to 0.19 by dividing 19 by 100: \[ 19 \div 100 = 0.19 \]
  2. **Step 2:** Multiply the decimal by the given number. Multiply 0.19 by 43: \[ 0.19 \times 43 = 8.17 \]
  3. **Step 3:** Conclude the result. State the final answer clearly: 19% of 43 is 8.17.


Following these steps ensures clarity and accuracy in your calculations. Always double-check each step to minimize errors and confirm your results.

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Most popular questions from this chapter

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$0.004$$

Write each fraction or decimal as a percent. Round to the nearest tenth of a percent. $$\frac{4}{5}$$

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. About \(\frac{2}{3}\) of U.S. households with televisions subscribe to a cabletelevision service.

Find the least common multiple of each pair of numbers. 21 and 35

Shade the given percent of a 100 -grid. Then express the shaded portion as a fraction and a decimal. $$4 \%$$
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