Problem 16 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth, if necessary. $$2.25$$

Step-by-Step Solution

Answer

2.25 as a percent is 225%.

Step 1: Understanding the Relationship between Decimals and Percents

To convert a decimal to a percent, we need to understand the basic relationship: 1 percent is 1 out of 100, or 0.01. Thus, converting a decimal to a percent involves expressing the decimal value as a number out of 100.

Step 2: Conversion from Decimal to Percent

To convert the decimal 2.25 to a percent, multiply it by 100. This is because 1 percent is equivalent to 0.01, and multiplying by 100 shifts the decimal point two places to the right.

Step 3: Calculation

Multiply the decimal 2.25 by 100: \[ 2.25 \times 100 = 225 \]So, 2.25 as a percent is 225%.

Step 4: Rounding the Result (If Necessary)

The result is 225%, which is already a whole number. Since rounding to the nearest tenth is not necessary here, the solution remains as it is.

Key Concepts

Percent Calculation

Calculating percents can seem challenging, but it's quite straightforward once you grasp the process. To convert a decimal into a percent, you essentially need to think of the decimal as being part of a whole or 100 percent. When you see a decimal like 2.25, you're seeing a number that represents 225 out of 100.

To achieve this conversion, the simplest way is by multiplying the decimal by 100. This shifts the decimal two places to the right, transforming your figure into a percent. So, for our example of 2.25:

• Multiply by 100: - \[2.25 \times 100 = 225\]
• The result is that 2.25 as a percent equals 225%.

If you ever need to go the other way, from percent to decimal, simply divide the percent by 100.

Decimal and Percent Relationship

Understanding the relationship between decimals and percents is like understanding two sides of the same coin. A decimal represents a fraction of a whole, while a percent represents parts per hundred.

Think of a percent as a decimal scaled up by 100. This means when you're converting from a decimal to a percent, you are determining how much of the total 100 it represents:

• 1 percent is equal to the decimal 0.01
• So, multiplying the decimal by 100 gives you the percent value.

This relationship is crucial in many areas of math, economics, and sciences. It's important to keep in mind that while a decimal may represent a quantity smaller than 1, its corresponding percent may appear considerably larger, such as 225% for 2.25.

Rounding Percents

Rounding is an essential skill to ensure figures are simple and easy to work with. Sometimes, after converting a decimal to a percent, you might end up with a long decimal percent like 45.6789%.

To make it more practical, it’s often rounded to a simpler figure. Rounding to the nearest tenth involves:

• Look at the hundredths place (the second digit after the decimal)
• If it’s 5 or more, round up. If it’s less than 5, round down.

For instance, 45.6789% becomes 45.7% because the digit in the hundredths place (7) is greater than 5.

Basic Math Skills

Building a strong foundation in basic math skills is essential when managing more complex concepts like decimal and percent conversions. These skills include understanding numbers, performing arithmetic operations, and recognizing patterns in math.

Here are a few basic skills that help with decimal-to-percent conversions:

• Multiplication and division (particularly by 100)
• Decimal place value understanding
• Rounding and estimating numbers for simplicity

These skills make tasks like converting decimals to percents less daunting and foster greater confidence in handling numbers across a variety of contexts.