Problem 81 - Algebra 1: Concepts and Skills

Question

Write the decimal as a percent. $$ 8.6 $$

Step-by-Step Solution

Answer

The decimal \(8.6\) as a percent is \(860\% \).

Step 1: Understand the Conversion

The first step is to understand the conversion from a decimal to a percent. We know that 1.00 as a decimal is the same as 100% as a percentage. This means multiplying the decimal by 100 will give us the percentage.

Step 2: Multiply the Decimal by 100

To change a decimal into a percentage, the decimal is multiplied by 100. Doing this with the given number \(8.6\) results in \(8.6 \times 100 = 860\).

Step 3: Add the Percentage Symbol

After performing the multiplication, it's important to remember to add the percentage symbol (%) to show the result is a percentage not a regular number. Thus, \(860\) becomes \(860\% \).

Key Concepts

Percentage Calculation

Calculating a percentage from a decimal is a straightforward process. It's essentially about understanding the relationship between a decimal and a percentage.
When you see a decimal, like 8.6, think of it as a part of a whole. To convert it to a percentage, which is a way to express parts of a hundred, you multiply it by 100. This conversion is crucial because it transforms the decimal into a more easily understood figure by putting it in terms everyone can relate to, i.e., parts per hundred.
Here’s a quick guide:

• Identify the decimal number you want to convert.
• Multiply that number by 100 to change it to a percentage.
• Add the percentage symbol (%) to indicate that it's a percentage.

By applying this method, you help communicate more effectively, as percentages are a common way of expressing data.

Multiplying Decimals

Multiplying decimals might sound intimidating at first, but it's not so different from multiplying whole numbers. The main difference comes from the placement of the decimal point afterward.
To multiply a decimal, you perform standard multiplication without focusing on the decimal place. Once you have the multiplication result, count the total number of decimal places in the numbers you multiplied. That count will dictate how many decimal places your answer should have.
For instance:

• Consider two numbers, such as 8.6. It has one decimal place.
• If you multiply it by 100, you're effectively shifting the decimal point two places to the right.
• The result is 860, which confirms your multiplication was accurate as you end with no decimal places in the integer 860.

Remember, practice makes perfect with decimals, and soon enough, you'll multiply decimals with confidence!

Basic Math Operations

Understanding basic math operations, like multiplication and addition, provides a foundation for more complex calculations. These operations are fundamental to practically every aspect of math.

Multiplication, particularly when dealing with decimals or converting to percentages, involves a few straightforward steps:

• Start by lining up numbers as you would with whole numbers.
• Ignore decimal points initially and focus on the multiplying process.
• Apply multiplication rules and then adjust for any decimal places based on the numbers used.

Adding symbols, like the percentage symbol (%), in your final results clearly indicates the type of number you're working with, helping to eliminate confusion in calculations. Recognizing these math basics helps tackle more challenging math problems that involve multiple steps or conversions, ensuring clarity and accuracy.