Problem 81 - Algebra 1: Concepts and Skills

Question

Write the given fraction, decimal, or percent in the indicated form. Write 0.674 as a percent.

Step-by-Step Solution

Answer

0.674 as a percent is 67.4%.

Step 1: Identifying the decimal

In this exercise, the decimal to be converted to a percentage is 0.674.

Step 2: Converting the decimal to a percentage

To convert a decimal to a percent, you multiply the decimal by 100. This means taking 0.674 and multiplying it by 100. This can be done using the equation: 0.674 * 100 = 67.4.

Step 3: Writing the result

After multiplication, the result is 67.4. This means that 0.674 as a percentage is 67.4%, because percent means 'per hundred'.

Key Concepts

Percent Conversion

Converting numbers into percentages is a common task that appears often in math and everyday life. Understanding the concept of percent conversion is essential for comparing values and understanding proportions.
At its most basic, percent conversion involves changing a number into a percentage to indicate its part out of a total 100. The word 'percent' comes from the Latin 'per centum', meaning 'by the hundred'. Hence, when you express a number as a percentage, you are essentially saying how much of 100 that number represents.
For example, 67.4% means 67.4 out of 100, or simply the fraction \( \frac{67.4}{100} \). This makes it easy to visualise and compare different quantities.

Multiplying Decimals by 100

The process of converting a decimal to a percent involves multiplying the decimal by 100. This step moves the decimal point two places to the right, effectively increasing the value by 100 times.
Consider the decimal 0.674. To convert this to a percentage:

• Identify the decimal: 0.674.
• Multiply by 100: \( 0.674 \times 100 \).
• The result is 67.4.

When you multiply 0.674 by 100, it becomes 67.4. The act of moving the decimal point two positions to the right is crucial, as it correctly transitions the decimal to a percentage figure.

Decimal to Percent Calculation

Calculating a decimal into a percentage is straightforward once you understand the process. After multiplying by 100, you obtain a percentage which is easily applicable in various scenarios, such as finance, statistics, and everyday percentage calculations like discounts.
To illustrate, let's follow through the example of converting 0.674:

• Start with your decimal number: 0.674.
• Multiply by 100 to change it into a percentage: \( 0.674 \times 100 = 67.4 \).
• Express this as a percentage by adding a percent sign: 67.4%.

This example shows that 0.674 as a decimal equals 67.4% when expressed in percentage format. This simple calculation allows for reliable comparisons and assessments, making it a key mathematical skill.