Problem 78 - Elementary Algebra

Question

$$ \text { Find } 2.5 \% \text { of } 18 $$

Step-by-Step Solution

Answer

0.45

Step 1: Convert the Percentage to a Decimal

To find a percentage of a number, first convert the percentage to a decimal. Move the decimal point two places to the left. For 2.5%, this becomes 0.025.

Step 2: Multiply the Decimal by the Number

Multiply the decimal by the number you want to find the percentage of. In this case, multiply 0.025 by 18.

Step 3: Perform the Multiplication

Carry out the multiplication: \[ 0.025 \times 18 = 0.45 \]

Key Concepts

Converting Percentage to Decimal

Understanding how to convert a percentage to a decimal is the first step in finding the percentage of a number. A percentage represents a fraction out of 100. For example, 50% means 50 out of 100.
To convert a percentage to a decimal, you simply move the decimal point two places to the left. This operation effectively divides the percentage by 100.

Let's take the percentage given in the exercise, 2.5%. By moving the decimal point two places to the left, 2.5% becomes 0.025.
Here's another example:

• Convert 75% to a decimal: Move the decimal two places left, resulting in 0.75.
• Convert 8% to a decimal: Moving the decimal two places left gives 0.08.

Practice this step with different percentages to become comfortable converting them to decimals.

Multiplication

Once you've converted the percentage to a decimal, the next step is to multiply. This step involves basic arithmetic.

In our exercise, we need to multiply the decimal 0.025 by the number 18. This can be broken down as follows:

• First, multiply as if they are whole numbers: 25 (from 0.025) times 18 equals 450.
• Next, account for the three decimal places (two in 0.025 and none in 18). Therefore, place the decimal point three places from the right in the product, making it 0.450, which simplifies to 0.45.

Thus, 2.5% of 18 equals 0.45. Multiplication is critical for finding percentages, so practice multiplying both decimals and whole numbers.

Basic Arithmetic

Basic arithmetic skills are fundamental in solving everyday percentage problems. These skills include addition, subtraction, multiplication, and division. Specifically for our problem, we focused on multiplication.

Cleaning up the steps with basic arithmetic ensures accuracy. Here is a quick recap that ties everything together:

• First, convert the percentage to a decimal (2.5% becomes 0.025).
• Then, multiply the decimal by the number in question (0.025 multiplied by 18).
• Use multiplication skills to find the product (0.45).

Understanding basic arithmetic helps you navigate through more complex math problems. Practice these operations often to build a strong math foundation.