Problem 27 - Introductory and Intermediate Algebra for College Students 4th

Question

Use the percent formula, \(A=P B: A\) is \(P\) percent of \(B,\) to solve Exercises \(27-42\) What is \(3 \%\) of \(200 ?\)

Step-by-Step Solution

Answer

The result of 3% of 200 is 6.

Step 1: Convert percentage to decimal

3% is equivalent to 0.03 in decimal form. Remember: to convert a percent to a decimal, divide it by 100. Thus, the equation now is \(A = 0.03 \cdot 200\).

Step 2: Multiply

Make a multiplication of 0.03 by 200. Using a calculator, multiplying 0.03 by 200 equals 6. So \(A = 6\).

Key Concepts

Percentage Calculation

Understanding percentage calculation is crucial in both mathematics and everyday life. A percentage is a way to express a number as a fraction of 100. In mathematical problems, it helps to identify ratios and proportions. The percent formula, \(A = P \times B\), where \(A\) is the result, \(P\) is the percentage, and \(B\) is the base number, is often used to calculate percentage-based questions. For example, to find out what 3% of 200 is, you use the percentage (3%) alongside the number (200). First, you need to convert the percentage into a decimal for easier calculation.

Decimal Conversion

Decimal conversion is a simple yet essential step when working with percentages. A percentage, being a fraction of 100, can be converted into a decimal by dividing by 100. This conversion makes it more convenient to perform multiplication or other operations. Let's use 3% as an example. When you divide 3 by 100, you get 0.03. Hence, 3% is equivalent to 0.03 in decimal form.

• Divide the percentage by 100.
• Use the decimal in calculations for accuracy.

This conversion is necessary for the percent formula to be applied effectively, as it standardizes the format across different operations.

Multiplication in Algebra

Multiplication is a fundamental operation in algebra and is crucial when working with formulas, such as the percent formula. Once you've converted the percentage into decimal form, the next step is to multiply the decimal by the given number.In the example given, you need to multiply 0.03 (the decimal form of 3%) by 200, which results in \(A = 0.03 \times 200\). When calculated, this product gives you 6.

• Use multiplication to merge the percentage and the base number.
• Verify your calculations for accuracy, especially when working with larger or more complex numbers.

This straightforward step pairs well with previous ones, helping us transition smoothly from percentage to practical results.