Problem 33 - Prealgebra

Question

Change each decimal to a percent. $$0.27$$

Step-by-Step Solution

Answer

0.27 as a percent is 27%.

Step 1: Understanding Percent Conversion

To convert a decimal to a percent, remember that 'percent' means 'per hundred'. Thus, you simply multiply the decimal by 100. This is because you are effectively determining how much the decimal value is out of 100.

Step 2: Perform the Multiplication

Take the decimal number, which is 0.27, and multiply it by 100 to find its percent form. This calculation is written as follows: \[ 0.27 \times 100 = 27 \]

Step 3: Add the Percent Symbol

Once you have the result from the multiplication, 27, the final step is to add the percent symbol (%) to indicate that the number is a percentage. Therefore, 0.27 as a percent is 27%.

Key Concepts

percent conversion

Converting a decimal to a percent is a straightforward process. The key idea here is around the meaning of the word 'percent.' It stems from "per centum," which means "by the hundred." Hence, when you want to convert a decimal into a percent, you are essentially determining what that decimal would be out of 100. To do this:

• Take your decimal number.
• Multiply it by 100.
• Add the percent symbol (%) after your result.

The multiplication by 100 repositions the decimal point two places to the right. For instance, converting the decimal 0.27 into a percent gives us 27% after multiplying by 100. This conversion process helps us express the same value in a different form that might be more intuitive to understand.

multiplying decimals

Multiplying decimals is an essential skill, especially when converting them to percentages. When you multiply a decimal by 100, you are adjusting its scale to express it as a percent. Here's how to handle multiplying decimals step-by-step:

• Ignore the decimals initially and perform the multiplication as if dealing with whole numbers.
• Count the total number of decimal places in the numbers you are multiplying.
• Place the decimal point in the answer, so the number of decimal places equals the sum of the decimal places counted from the original numbers.

For example, if you multiply 0.27 by 100, initially consider 27 x 100:

• $27\; imes\; 100\; =\; 2700$

Then adjust for the decimal by moving the point two places to the left (as 0.27 has two decimal places), giving 2700 with two decimal places moved left, resulting in 27.

understanding percentages

Percentages are a way of expressing numbers as parts out of 100. They allow for easy comparison between different values, which is especially useful in statistical analysis, data presentation, and daily applications like discount calculations. Why are percentages important?

• They standardize numbers, making them easier to compare.
• Common in financial contexts, such as calculating interest rates or comparing company performance.
• Used in statistics to present proportions and share information effectively.

Knowing how to convert decimals to percentages is crucial because it lets you communicate information more clearly. For example, understanding that 0.27 is equivalent to 27% provides a clearer view of the proportion or the part of a whole that the number represents. It gives the number a place relative to 100, making it more accessible and understandable for everyone.