Problem 34 - Algebra 1

Question

Find the percent of a number. $$1.25 \% \text { of } 90$$

Step-by-Step Solution

Answer

The 1.25% of 90 is 1.125.

Step 1: Convert Percentage to Decimal

Firstly, to calculate a percentage of a number, the percentage needs to be converted into a decimal. Here, 1.25% should be divided by 100 to convert it into a decimal. Thus, \(1.25 \div 100 = 0.0125\).

Step 2: Multiply by Number

Next, multiply the number, 90, by the decimal 0.0125. This is done using simple multiplication, \(90 \times 0.0125 = 1.125\).

Key Concepts

Decimal Conversion

To find the percentage of a number, the first step is to convert the percentage into a decimal. This is done by dividing the percentage by 100. Why 100? Because percent, derived from the Latin "per centum," means "per hundred." Hence, to convert a percentage to a decimal, you're effectively figuring out how many times the percentage fits into 100.

For example, with 1.25%, we perform the division:

• 1.25 divided by 100 equals 0.0125

This transformation is crucial for subsequent mathematical operations. Remember that any percentage can be converted into a decimal by this simple division method. It's a foundational skill in many math tasks!

Decimal Multiplication

Once you have converted the percentage into a decimal form, the next step involves multiplication. You multiply the decimal by the given number to find the percentage of that number. Decimal multiplication is simple if you follow the basic rules: align the numbers, multiply as whole numbers, and then position the decimal point in the result based on the total number of decimal places in the factors.

If we look at the problem at hand, you take the decimal 0.0125 and multiply it with 90:

• 0.0125 multiplied by 90 equals 1.125

Remember, after performing the multiplication, ensure that any remaining decimal places are included in the final answer. Precision is important in decimal operations to retain accuracy in your results.

Basic Arithmetic Operations

Arithmetic operations such as addition, subtraction, multiplication, and division are the building blocks of math. In percentage calculations, multiplication is particularly useful. This operation allows us to scale a number by a given decimal factor obtained from percentage conversion.

Here is a quick refresher on multiplication:

• Arrange the numbers with the number having fewer digits on the bottom.
• Start multiplying each bottom digit with each top digit. Work column by column.
• Sum up all the results, shifting them by one place left as you move to the higher digit of the bottom number.
• Adjust your result by placing the decimal point where it belongs.

In the context of our exercise, once you know the correct position for the decimal, the multiplication is straightforward. This clarity in basic arithmetic solidifies understanding, making calculations less daunting and more straightforward.