Problem 49 - Prealgebra

Question

Express each decimal as a percent. $$0.27$$

Step-by-Step Solution

Answer

0.27 as a percent is 27%.

Step 1: Understanding the Problem

The task is to express the decimal 0.27 as a percent. A percent is a way of expressing a number as a fraction of 100. Hence, converting a decimal to a percent involves some basic multiplication.

Step 2: Multiplying by 100

To convert the decimal 0.27 to a percentage, multiply it by 100. In mathematical terms, this is represented as 0.27 × 100.

Step 3: Calculating the Product

Carrying out the multiplication: 0.27 × 100 = 27. This is because multiplying by 100 moves the decimal point two places to the right.

Step 4: Adding the Percent Symbol

Since multiplying the decimal by 100 gives the numeric value associated with the percent, simply add the percent symbol (%). Thus, 0.27 becomes 27%.

Key Concepts

Fraction of 100

When someone refers to a fraction of 100, they are talking about how a part of something relates to an entire or whole that is divided into 100 equal parts. This concept is at the heart of understanding percentages. Think of it this way: If you have a whole pie, and it is cut into 100 equal pieces, each piece represents 1% or one part per hundred. Similarly, when we express a decimal like 0.27 as a percentage, we're essentially asking how this decimal relates to the whole when the whole is broken down into 100 parts. Decimals and fractions can be relatable when you consider them on this scale of 100. For instance, the decimal 0.27 can initially seem abstract until you realize it represents 27 pieces out of 100. This simple understanding forms the basis for converting decimals to percentages.

Multiplying Decimals

Multiplying decimals might sound complicated, but it’s straightforward once you get the hang of it. To convert a decimal to a percent, you're going to multiply by 100, which is a common practice in mathematics. Here’s how it works in practice with the example of 0.27:

• First, consider the decimal number (in this case, 0.27).
• Multiply it by 100. Mathematically, this is shown as 0.27 \( \times \) 100.
• When you multiply by 100, you're essentially moving the decimal point two places to the right.

Now transformation happens: 0.27 becomes 27. This step represents a critical part of turning a decimal into a percentage. It’s helpful because it highlights the connection between a decimal and its role as a fraction of 100. After all, 27 is much easier to relate back to a percentage than 0.27 on its own.

Percent Symbol

The percent symbol (%) is a crucial marker indicating that a number is a percent, not a plain value. It carries the literal meaning of 'per one hundred.' After you have converted your decimal by multiplying by 100 (such as moving from 0.27 to 27), the only thing left to complete the transformation to a percentage is to add the percent symbol. Consider why the percent symbol is important:

• The symbol serves as a reminder that the number reflects a fraction of a whole (or 100), not an absolute quantity.
• It communicates clearly in equations and results that you are using percentages, which have a different base than other numbers.

To put it all together with our example, after converting 0.27 to 27 through multiplication, we simply append the % symbol to get 27%. This completes the process and gives you the final expression of the decimal as a percentage.