Problem 52 - Prealgebra

Question

Write each decimal as a percent. $$0.58$$

Step-by-Step Solution

Answer

0.58 is equivalent to 58%.

Step 1: Understand the Relationship

To convert a decimal to a percent, recall that percent means 'per hundred.' This implies we need to express the decimal as an equivalent fraction with a denominator of 100.

Step 2: Multiply by 100

To convert the decimal 0.58 into a percent, multiply 0.58 by 100. This is equivalent to shifting the decimal point two places to the right.

Step 3: Calculation

Perform the multiplication: \(0.58 \times 100 = 58\).

Step 4: Write as a Percent

After performing the multiplication, we find that 0.58 is equivalent to 58 percent. Thus, we write it as 58%.

Key Concepts

Decimals to Percents

When converting decimals to percents, we're essentially finding out how much of a whole number (in our case, 100) the decimal represents.
To put it simply, "percent" means "per hundred." By converting, we want the number to show how many parts out of 100 it takes.

• The simple trick is to take the decimal number and move the decimal point two places to the right.
• This is mathematically the same as multiplying the number by 100.

Imagine you have 0.58. By moving the decimal point to the right by two places, you get 58. Hence, 58 is actually 58 out of 100, or 58%. This method works for any decimal number you have and quickly gives you a percentage amount.

Mathematical Operations

In mathematics, an operation is a calculation applied to numbers to obtain a result. The basic operations include addition, subtraction, multiplication, and division.
To carry out a percent conversion, we focus on multiplication.

• Here, we use multiplication to scale the decimal by 100 since a percent is the number out of 100.
• This conversion transforms the decimal representation into one that's compatible with percentage interpretation.

Practicing this operation of multiplying by 100 is crucial. For example, when you convert 0.58, multiplying by 100 gives you 58. This simplifies the decimal into a percent that can be easily compared and utilized in real-life applications.

Fraction Conversion

At its core, converting decimals to percents has similarities to converting fractions.
Even though we begin with a decimal, the end goal is to express it as a part of a whole, much like a fraction.

• In the case of decimal to percent conversion, the denominator of our fraction becomes 100.
• This way, the decimal 0.58 becomes 58/100, which we read directly as 58%.

This approach helps visualize the process. In this sense, percent conversion is a form of fraction conversion where the comparison is always out of a consistent number: 100.
Once you understand the process, it'll be easy to manage different numerical transformations between decimals, fractions, and percents.

Numerical Expressions

Numerical expressions involve numbers and operation symbols combined to represent a specific value or calculation.
When converting decimals to percents, the main numerical expression is the multiplication of the decimal by 100.

• Each conversion follows this simple expression: \[\text{Decimal} \times 100 = \text{Percent}\]
• Inserting the number 0.58 into this equation gives: \[0.58 \times 100 = 58\]

Once you multiply, the result right side is your percent value.
This illustrates how converting decimals into percents can be seamlessly expressed as a clear and easy calculation. Understanding this mathematical expression will boost your confidence in swiftly managing conversions in a variety of contexts.