Problem 25 - Elementary Algebra

Question

For the following problems, convert each percent to a decimal. $$ 18.6 \% $$

Step-by-Step Solution

Answer

Question: Convert 18.6% to a decimal. Answer: 0.186

Step 1: Identify the given percentage

The given percentage is 18.6%.

Step 2: Divide the percentage by 100

To convert the percentage to a decimal, divide 18.6 by 100: $$ \frac{18.6}{100} $$

Step 3: Simplify the expression

Calculating the division, we get: $$ 18.6 \div 100 = 0.186 $$

Step 4: Write the final answer

The decimal equivalent of 18.6% is 0.186.

Key Concepts

Decimal Representation

Decimals are a way of representing numbers that are not whole. They are used to express values that might be smaller than one, such as parts of a whole.
For example, the decimal 0.186 is a representation of the number eighteen and six-tenths divided by 100, which is exactly how 18.6% is converted into a decimal.
In a decimal system, each digit has a place value that depends on its position relative to the decimal point.

• The first position to the right of the decimal point signifies tenths.
• The next position is hundredths, followed by thousandths, and so on.

Understanding decimals is key to working with percentages, as percentages are just a specific type of decimal that is multiplied by 100.

Division in Mathematics

Division is one of the basic operations in mathematics. It involves splitting a number into equal parts.
When converting percentages to decimals, division is used because percentages are inherently related to the number 100.
Performing division by 100 is a simple mathematical step that allows us to translate percentage values into their decimal form.
Let’s break it down:

• Identify the number to be divided, which is the percentage value in this context.
• Divide this number by 100, which shifts the decimal point two places to the left.

For example, 18.6 divided by 100 results in 0.186. This helps in directly visualizing how a part relates to the whole without the percentage sign.

Percentage Calculation

Percentages represent fractions of 100 and are a practical way to express proportions.
Learning how to convert percentages to decimals is vital for accurate calculations in both everyday tasks and statistical data interpretation.
To calculate a percentage, follow these basic steps:

• Take the given value and understand it signifies parts per hundred.
• Divide the value by 100 to remove the percentage notation.

This is useful in various mathematical problems, where a more straightforward decimal form can make additional calculations simpler and more efficient.
For instance, converting 18.6% into 0.186 aids in further computations if you're adding, subtracting, multiplying, or dividing it by other numbers.