Problem 22 - Prealgebra

Question

Change each decimal to a percent. $$0.34$$

Step-by-Step Solution

Answer

0.34 as a percent is 34%.

Step 1: Understanding the Concept

To convert a decimal to a percent, we need to understand that a percent represents a number out of 100. This means we take the decimal and adjust it so that it fits this 'out of 100' requirement.

Step 2: Transforming the Decimal

Convert the decimal to a percent by multiplying it by 100. This changes the scale of the number from being out of 1 to being out of 100. For our decimal of 0.34, we do the following calculation: \(0.34 \times 100\).

Step 3: Calculating the Result

Carry out the multiplication from the previous step. Therefore, \(0.34 \times 100 = 34\). This gives us the number as a percent.

Step 4: Applying the Percent Symbol

After calculating the result, we need to include the percent sign (%) to indicate that we have converted the decimal into a percent. The final answer is 34%.

Key Concepts

Percent

Understanding the concept of a percent is essential when dealing with conversions. A percent is a way to express a number as a fraction of 100. Instead of handling large numbers, we reduce or magnify them to fit within a 0 to 100 scale.
This makes comparison and comprehension easier across various applications, like calculating discounts or comparing success rates in experiments.
By definition, 1% is equivalent to 1 out of 100, or in decimal form, 0.01. Hence, converting numbers into percent form is helpful in numerous practical scenarios.

Decimal Multiplication

At the core of converting a decimal to a percent lies the process of decimal multiplication. This calculation stretches the decimal to fit into the percent format.
To perform this operation, simply multiply the decimal number by 100.

• The decimal represents a part of a whole, or out of 1.
• By multiplying by 100, you change its domain from out of 1 to out of 100.
• For instance, with our example of 0.34, the multiplication step looks like this: \(0.34 \times 100 = 34\).

Through this multiplication, we scale the decimal to its equivalent percent.

Mathematical Conversion Steps

Converting decimals to percents involves a series of straightforward calculation steps, making the process simple and repeatable.
Here's a breakdown of these steps:

• Step 1: Recognize that a percent means "per hundred," so identify your decimal.
• Step 2: Multiply the decimal by 100 to adjust its scale from a base of one to a base of hundred.
• Step 3: Perform the multiplication to get the numeric result.
• Step 4: Add the percent sign (%) to denote that the number is now a percentage.

By following these steps, you can successfully convert any decimal into a percent!

Percent Sign

Once you've calculated the decimal-to-percent conversion, the final step is to apply the percent sign (%). This symbol is crucial as it signals that the number is now a percentage.
Including the percent sign transforms your numeric result into a clear and universally understood format.
For the example decimal of 0.34, after converting it to 34, adding the percent sign gives us 34%.
The percent sign is a small yet important detail that ensures effective communication of the mathematical conversion.