Problem 38 - Elementary Algebra

Question

Convert each percent to its decimal equivalent. $$ 215 \% $$

Step-by-Step Solution

Answer

215% as a decimal is 2.15.

Step 1: Understanding Percentages

To convert a percentage to a decimal, you need to understand that a percentage is a number out of 100. So, 215% means 215 per 100.

Step 2: Dividing by 100

Now, take the percentage value, which is 215, and divide it by 100. This will convert the percentage into a decimal. The calculation is as follows:\[ 215 \div 100 = 2.15 \]

Step 3: Writing the Decimal

After dividing, the result is 2.15. This is the decimal equivalent of 215%.

Step 4: Verification

To verify, you can multiply the decimal (2.15) by 100 to see if you get back the original percentage:\[ 2.15 \times 100 = 215 \] This confirms that the conversion is correct.

Key Concepts

Decimal Equivalent

When we talk about the decimal equivalent of a percentage, we are referring to how the percentage value is expressed as a decimal number. Understanding the concept of a decimal equivalent is crucial, as it allows us to work more easily with various calculations, such as multiplication or division.

• Percentages are based on the number 100.
• A decimal number can show the same value in a different form, often making calculations simpler.

For instance, with 215%, we convert this to its decimal equivalent to make its usage more flexible with different mathematical operations. In the practical world, this knowledge helps in financial calculations and data interpretation.

Division by 100

The process of converting a percentage to a decimal primarily revolves around division by 100. This step is pivotal because percentages describe a relationship concerning the number 100.

• To transform a percentage into a decimal, divide the percentage by 100.
• This eliminates the percentage aspect and presents pure numerical values that are useful in diverse applications.

For example, converting 215% involves the calculation: \[215 \div 100 = 2.15\] This simple division aligns with the fact that percentages are essentially fractions of a whole, represented by 100. By dividing, we can see clearly what part of the whole the percentage represents in decimal form.

Percentages to Decimals

Converting percentages to decimals is a common mathematical operation that simplifies many calculations. This process is essential for accurate computations, be it financial modeling, data analysis, or scientific calculations.

• Percentages allow comparisons in relation to 100, while decimals enable precision and straightforward arithmetic operations.
• Converting is straightforward: remove the percentage sign and divide the number by 100.

By converting 215% to a decimal, we perform the operation: \[215 \div 100 = 2.15\] Using decimals instead of percentages can considerably streamline tasks where exact figures are crucial.

Verification of Conversion

Once we convert a percentage to a decimal, verifying the conversion ensures accuracy. This is done by reversing the process—changing the decimal back to the percentage—and checking if it matches the original percentage.

• Multiply the decimal by 100 to retrieve the original percentage value.
• Verification confirms that no errors were made during the conversion process.

For instance, with 2.15 as the decimal equivalent, the multiplication \[2.15 \times 100 = 215\] shows that the conversion is indeed correct. Verification of conversion is a good practice to guarantee the integrity of your mathematical operations.