Problem 13 - Elementary Algebra

Question

For the following problems, convert each decimal to a percent. $$ 0.36 $$

Step-by-Step Solution

Answer

Question: Convert the decimal 0.36 to a percentage. Answer: 36%

Step 1: Multiply the decimal by 100#

To convert the decimal 0.36 to a percentage, multiply it by 100: $$ 0.36 \times 100 = 36 $$

Step 2: Add the percent sign#

After multiplying by 100, we have 36. Now, we add the percent sign to it: $$ 36 \Rightarrow 36\% $$ So, the decimal 0.36 is equal to 36%.

Key Concepts

Percent Calculation

Converting a decimal to a percent is an essential mathematical skill. It involves understanding that a percentage is simply a way to express a number as a part of 100. When you're asked to convert a decimal like 0.36 into a percent, you need to translate this number into its equivalent parts of 100.

• Start with the decimal: 0.36.
• Multiply it by 100, since percent means "per hundred".
• This gives you the number of parts out of 100, which is the percentage form.

Hence, when you multiply 0.36 by 100, the result is 36. Thus, 0.36 as a percentage is written as 36%. The key takeaway is remembering the multiplication by 100 is what transforms the decimal to a percent, providing the clear format we use daily in various calculations, like sales tax and interest rates.

Multiplying Decimals

Multiplying decimals might seem tricky at first, but it's a straightforward process once you understand the basics. Let's go through the steps using the example of converting 0.36 to a percent as shown in the original problem.
First, treat the decimal as if it were a whole number during multiplication. For instance, multiplying 0.36 by 100 involves multiplying 36 by 100 first, ignoring the decimal point temporarily.

• Multiply 36 by 100 to get 3600.
• Now, count the number of decimal places in the original decimal. In 0.36, there are two decimal places.
• Divide the product (3600) by 100 (as you virtually added two zeros to 36 when ignoring the decimal places), resulting in the final product of 36.

This method ensures that you correctly scale the decimal into a percentage. Becoming comfortable with these basic steps can help simplify more complex calculations involving decimals.

Mathematics Conversion

Mathematics conversion is about changing numbers from one form to another in a way that maintains their equality. When dealing with decimal to percent conversions, the focus is on maintaining equivalency between numerical representations.
In real-world applications, understanding these conversions is crucial as it allows for better interpretation of data and simpler communication of mathematical ideas. For example, grasping that 0.36 and 36% are equivalent provides insights not just into the number itself but into its magnitude relative to 100 parts, making it easy to visualize and utilize in various situations.
Key points to remember when performing these conversions include:

• Identify the type of conversion required.
• Use the appropriate mathematical operations - such as multiplication by 100 for decimal to percent conversions.
• Pay attention to details like decimal placement and correct unit representation (like using the % symbol).

Successfully converting decimals to percentages strengthens overall numerical literacy and enhances analytical skills critical in both academic and everyday environments.