Problem 75 - Elementary Algebra

Question

Convert to a percent. 0.055

Step-by-Step Solution

Answer

0.055 is equal to 5.5%.

Step 1: Understanding the Decimal

To convert a decimal to a percent, you need to understand the value of the decimal. The number 0.055 is in decimal form and represents a value less than one.

Step 2: Multiplication by 100

To convert the decimal 0.055 to a percentage, multiply it by 100. This is because percent means 'per hundred.' The equation is: \[ 0.055 \times 100 = 5.5 \]

Step 3: Assignment of Percent Symbol

After multiplying the decimal by 100, add the percent symbol (%) to represent the value as a percent. So, 5.5 becomes 5.5%.

Key Concepts

Decimal to Percent

Converting a decimal to a percent may seem tricky at first, but it can be simplified with a little understanding. The essential idea is that a decimal number represents a fraction of one. For example, the decimal 0.055 implies that it's 55 thousandths of a whole number. In more simple terms, 0.055 is less than 1, which is why we need to make it fit within a scale of 100 to express it as a percent.

Visualizing the number line, imagining 0, 0.5, and 1 can be helpful. Decimals are basically parts of a hundred. So, transforming 0.055 into a percent will make it easier to understand in the context of everyday situations, like statistics or financial figures. Remember, the purpose of converting decimals to percentages is to express the figure as a portion of 100. This makes it universally understandable.

Multiplying by 100

When converting a decimal to a percent, an important step is multiplying by 100. The word 'percent' actually means "per hundred," which is why multiplication by 100 is necessary.

Let's dive into the mathematics of it: when you have a decimal like 0.055, multiplying it by 100 shifts it from being a fraction of a single unit to a fractional part of 100. This is represented mathematically as:

• 0.055 \( \times \) 100 = 5.5

Hence, the underlying concept here is simple; the decimal scale is transformed to the percentage scale once multiplied by 100. This step is crucial, as it makes the number ready to be denoted as a percentage. Multiplying by 100 isn't just a formula to memorize—it's the bridge that lets you translate decimal numbers into percentages accurately.

Always remember, multiplying by 100 is the magic step that says: here's your number out of 100, not out of 1.

Percent Symbol

Once you've multiplied the decimal by 100, the next steps are easy breezy. Adding the percent symbol \( \% \) finalizes the conversion. Let's examine why it's so critical.

The percent symbol tells you the number you've derived is out of 100, making it universally readable and applicable. So after achieving the value of 5.5 from our multiplication, placing a percent symbol at the end makes it 5.5%.

• This tiny symbol means a lot; it removes ambiguity.
• It confirms that your decimal-to-percent conversion is complete.

In everyday situations, this symbol is pivotal—whether you're deciphering interest rates, data figures, or even sales tax. The percent sign serves to present a part of the whole in the simplest terms possible. As a rule of thumb, don't forget to add the \( \% \) after your calculation—it is the essential concluding step that confirms you have successfully converted your decimal to a percent.