Problem 18 - Elementary Algebra

Question

For the following problems, convert each decimal to a percent. $$ 5.875 $$

Step-by-Step Solution

Answer

Question: Convert the decimal 5.875 to a percent. Answer: 587.5%

Step 1: Identify the given decimal

The given decimal is $$5.875$$.

Step 2: Multiply by 100

To convert the decimal to a percent, we will multiply $$5.875$$ by $$100$$. So, the calculation will look like this: $$5.875 \times 100 = 587.5$$

Step 3: Add the percent symbol

Now, we will add the percent symbol ("%") to the result obtained in step 2. $$587.5 \%$$

Step 4: Final Answer

The decimal $$5.875$$ converted to a percent is $$587.5 \%$$.

Key Concepts

Percent Calculation

Understanding how to convert decimals to percents is an important skill in mathematics. A percent represents a number out of 100, meaning it is essentially a fraction with a denominator of 100. To calculate the percent from a decimal, you need to multiply the decimal by 100.

For instance, to convert the decimal 5.875 to a percent:

• First, you multiply it by 100, which shifts the decimal point two places to the right.
• After multiplying, you get 587.5, which means 5.875 is equivalent to 587.5%.
• Finally, add the percent symbol (%) to the result, indicating you've completed the conversion.

This process helps in quickly expressing quantities in terms of percent, which can be more intuitive for understanding proportions and comparisons.

Multiplying Decimals

The act of multiplying decimals often causes worry among students, but it's simpler with a little practice. Multiplying decimals involves calculating as you would for whole numbers, then placing the decimal in the right position after the calculation.

Here's how you can do it:

• Multiply the numbers normally, ignoring any decimal points.
• Count the total number of decimal places in the numbers you began with.
• After multiplication, place the decimal point in your answer, moving from the right, according to the total number of decimal places you counted.

Thus, in our example of converting 5.875 to a percent, the multiplication by 100 simplifies to moving the decimal two places right, resulting in 587.5. By understanding this process, multiplying decimals becomes an easier and quicker calculation.

Mathematical Conversions

Mathematical conversions allow us to translate numbers between different forms, like from decimals to percents. This is particularly useful in real-world applications, where different formats are needed for different circumstances.

Key steps involved in converting decimals to percents are:

• Recognize the initial format: Here, start with a decimal number, such as 5.875.
• Convert by multiplying by 100: This is done because percent means per hundred, aligning the decimal with this understanding.
• Finalize with the percent symbol: Once multiplied, append "%" to signify the conversion is complete.

Understanding these conversion steps allows you to swiftly change numbers into a more practical or required form. It's a key skill in both academic problems and practical scenarios, enabling better data interpretation and communication.