Problem 55 - Prealgebra

Question

Write each decimal as a percent. $$2.04$$

Step-by-Step Solution

Answer

2.04 as a percent is 204%.

Step 1: Understanding the Problem

The task is to convert a decimal number, 2.04, into a percentage. A percentage is a way to express a number as a part of 100.

Step 2: Converting Decimal to Percentage

To convert a decimal to a percentage, multiply the decimal by 100. This is because 'percent' means 'per hundred', so multiplying by 100 shifts the decimal point two places to the right.

Step 3: Execute the Conversion

Multiply 2.04 by 100. \(2.04 \times 100 = 204\).

Step 4: Write the Result with the Percentage Symbol

After multiplying, add the percentage symbol (%) to the result. So, 204 becomes 204%. Thus, 2.04 as a percent is 204%.

Key Concepts

Decimal Conversion

Converting decimals into percentages is a fundamental math skill. It simplifies comparing different quantities and can express values in a familiar format. A decimal is a fraction whose denominator is a power of ten. For example, 2.04 is essentially the same as 204/100. To express a decimal as a percentage, you multiply the decimal by 100. This shifts the decimal point two places to the right, enabling you to express the number in terms of hundreds.

For example:

• 2.04 as a percentage becomes 204% because 2.04 multiplied by 100 is 204.
• This illustrates how percentages can reflect the magnitude of a quantity compared to 100.

Remember, the '%' symbol is crucial because it signifies that the number is a fraction of 100. Decimal conversion is widely applicable, including in finance, statistics, and everyday measurements.

Mathematical Expressions

Mathematical expressions encapsulate various numeric calculations and operations. They are foundational to understanding and performing conversions, like turning decimals to percentages. An expression can include numbers, variables, and operation symbols such as addition, subtraction, multiplication, and division.

When you see an expression like 2.04 \( \times \) 100, it represents a process or set of operations meant to yield a particular result—in this case, converting a decimal to a percentage. By understanding expressions, you can manipulate numbers effectively to achieve desired outcomes.

Mathematical expressions are concise and powerful tools. They help to break down complex problems into manageable tasks, facilitating deeper understanding in mathematical reasoning and problem-solving.

Basic Arithmetic

Basic arithmetic is the cornerstone of mathematics, dealing with essential operations such as addition, subtraction, multiplication, and division. It is critical in converting decimals to percentages because multiplying the decimal by 100 is an arithmetic operation.

Here's how basic arithmetic operations apply:

• Multiplication: In the example of converting 2.04 to a percentage, multiplication is used directly: 2.04 \( \times \) 100 = 204.
• This straightforward calculation demonstrates the concept of scaling the number by a factor of 100 to find its equivalent percentage.

Having a good grasp of basic arithmetic enables solving various mathematical problems efficiently. It’s what's used in daily life, from calculating the bill at a restaurant to managing finances.