Problem 38 - Prealgebra

Question

Express each decimal or fraction as a percent. Round to the nearest tenth,if necessary. $$3.21$$

Step-by-Step Solution

Answer

3.21 as a percent is 321%.

Step 1: Understanding the Decimal to Percent Conversion

To convert a decimal to a percentage, multiply the decimal by 100. This is because 'percent' means 'per hundred.'

Step 2: Performing the Calculation

Multiply the decimal number 3.21 by 100: \[ 3.21 imes 100 = 321 \]

Step 3: Final Answer and Rounding

In this case, the calculation results in 321. Since we need to round to the nearest tenth and there are no decimal places, the result is already at its simplest form.

Key Concepts

Percent Conversion Basics

The term "percent" is derived from the Latin phrase "per centum," which translates to "by the hundred." In mathematics, a percent is a way of expressing a number as a fraction of 100. This allows for easy comparison of different quantities. For example, saying 25 percent is akin to saying 25 out of 100.

When converting a decimal to a percent, you multiply the decimal by 100. This is because you are essentially finding out how many parts out of one hundred the decimal represents. After multiplying, you add the percent sign (%) to indicate that the number is a percent.

• To convert 3.21 to a percent, multiply by 100: \[ 3.21 \times 100 = 321 \]
• The result, 321, is now expressed as a percent: 321%.

This simple conversion technique allows for a straightforward transition from a decimal to a percentage form.

Rounding Decimals

Rounding decimals involves adjusting a number to its nearest specified place value. It helps in making numbers simpler and more precise for estimation purposes. The fundamental rule of rounding is to look at the number directly to the right of the rounding place.

• If this number is 5 or more, round up by adding one to the rounding place.
• If the number is less than 5, the rounding place stays the same.

In the case of 321, if we need to round to the nearest tenth, we first note that the number doesn't have any digits after the decimal point. This means it's already in simplest form regarding decimals.

Rounding won't affect 321 because there are no digits beyond the tens place, making it straightforward in this example. It's essential to understand rounding, as it can significantly impact calculations and interpretations, especially when more digits are involved.

Understanding Multiplication in Conversion

Multiplication plays a crucial role in converting decimals to percents. The process involves adjusting the decimal value to scale it up by a factor of 100. When we multiply a decimal by 100, it essentially shifts the decimal point two places to the right.

• For instance, the number 3.21 multiplied by 100 transforms into 321, moving two decimal places to the right: \[ 3.21 \times 100 = 321 \]
• This multiplication by 100 ensures the decimal is expressed as parts of a hundred, hence making it a percent.

Understanding multiplication in this context simplifies the conversion process. It provides a straightforward method to grasp how decimals fit into larger scales, allowing students to communicate numerical values effectively in terms of percentages.