Problem 26 - Prealgebra

Question

Change each decimal to a percent. $$0.54$$

Step-by-Step Solution

Answer

0.54 is 54%.

Step 1: Understand the Conversion

To convert a decimal to a percent, you need to shift the decimal point two places to the right. This is because 'percent' means 'per hundred', so we're multiplying by 100.

Step 2: Perform the Conversion

Shift the decimal point in 0.54 two places to the right. This changes 0.54 to 54.

Step 3: Add the Percent Sign

Once you have moved the decimal, add the percent sign (%) to the number to express it as a percentage.

Step 4: Confirm the Result

After shifting the decimal and adding the percent sign, 0.54 becomes 54%. This represents that 0.54 as a percentage is 54%.

Key Concepts

Percentages

The concept of percentages is fundamental in mathematics and everyday life. A percentage represents a part of a whole divided into 100 equal parts. When we talk about percentages, we're essentially discussing how many parts of 100 something contains. If you have a value expressed in decimal, converting it to a percentage involves showing that number as how much out of 100 it is. For example, if you have a decimal like 0.54, it means that for every 1 unit, you have 0.54 of something. Converting this decimal to a percentage highlights how this number fits into a total of 100. Thus, decimals and percentages are just different ways to express parts of a whole.

Multiplying Decimals

Multiplying decimals is a key mathematical skill that enhances one's ability to transform numbers, such as converting decimals to percentages. When we convert a decimal into a percentage, we need to multiply the decimal by 100. This mathematical operation highlights the relationship where percentages are a way of expressing values as parts of a whole of 100. For instance:

• The decimal 0.54 multiplied by 100 is equal to 54.

This computation signifies that 54 is simply 0.54 represented in percentage terms. Working with decimals can seem daunting at first, but understanding the straightforward process of multiplication by 100 simplifies the conversion to percentages. It's essential to master this operation because it frequently appears in various mathematical contexts, enhancing both numerical fluency and problem-solving skills.

Decimal Point Movement

Moving the decimal point is a simple yet powerful technique that makes calculations with decimals much easier, especially when converting to percentages. To convert a decimal to a percentage, we move its decimal point two places to the right. This action is equivalent to multiplying the decimal by 100. Here's how to do it step by step:

• Start with the decimal number, for example, 0.54.
• Move the decimal point two places to the right. For 0.54, the decimal point moves past the 5 and the 4, turning it into 54.

This movement transforms the decimal into its percentage equivalent swiftly and efficiently. Once moved, simply add a percent sign to display the number as a percentage. Understanding decimal point movement simplifies many calculations and provides a quick strategy for conversions in mathematics.