Problem 58 - College Algebra and Calculus: An Applied Approach

Question

Use a calculator to solve.\(147 \%\) of 22

Step-by-Step Solution

Answer

The answer is 32.34.

Step 1: Understand the Problem

It is asked to find 147% of 22. The percentage is a proportion out of 100. Therefore, this implies we need to find out what 147 out of 100 parts of 22 would be.

Step 2: Convert Percentage to Decimal

The next step is converting the percentage into a decimal number. This is done by dividing the percentage by 100. So, 147% becomes 1.47 when divided by 100.

Step 3: Calculate the percentage of the number

Now, multiply this decimal number by the original number to get the percentage of the number. So, multiply 1.47 by 22. The result is 32.34.

Key Concepts

Decimal Conversion

To find a percentage of a number, we first need to convert the percentage into a decimal. This process is known as decimal conversion. Think of a percentage as a fraction out of 100. For instance, 147% means 147 out of 100. By dividing by 100, you convert the percentage to a decimal. For example, 147% becomes 1.47 as a decimal. This is a crucial step in percentage calculation and is applicable across various mathematical situations. Remember, moving a percentage to a decimal is simply shifting the decimal point two places to the left.

• This works with any percentage value.
• It simplifies further calculations, such as multiplication.

Multiplication

Once you have converted the percentage into a decimal, the next step is multiplication. Multiplication allows you to calculate the exact percentage value from a number. In this case, you take the decimal equivalent of the percentage and multiply it by the number you want the percentage of. Here, with 147% converted to 1.47, you multiply this by 22: \[1.47 \times 22 = 32.34\]This equation gives you the percentage value of the number.A strong grasp of multiplication is key:

• It is essential for finding percentages.
• It is used in a variety of real-world applications such as finance and data analysis.

Calculator Usage

Calculators are handy tools for quickly and accurately solving mathematical problems. In this case, a calculator helps verify the accuracy of percentage calculations effortlessly. To solve the problem using a calculator, you start by entering the decimal you obtained: 1.47. Then, multiply it by the original number, 22. Just press the multiplication button on the calculator, input the number 22, and hit equals. Using calculators is beneficial as they:

• Save time in solving complex calculations.
• Reduce human error, ensuring accuracy.
• Can handle large numbers and complex operations.

By using calculators effectively, you can ensure that the results are reliable, especially when working with multiple steps or larger numbers.