Problem 288 - Intermediate Algebra

Question

In the following exercises, convert each decimal to a percent. $$ 3 $$

Step-by-Step Solution

Answer

300%

Step 1: Understand the Problem

The task is to convert the given decimal number into a percentage. In this case, the decimal number is 3.

Step 2: Convert Decimal to Percentage

To convert a decimal to a percent, multiply the decimal by 100. Mathematically, this is written as: $$ 3 \times 100 $$

Step 3: Calculate the Result

Perform the multiplication: $$ 3 \times 100 = 300 $$

Step 4: Add the Percentage Symbol

Finally, add the percentage symbol to the result: $$ 300 \% $$

Key Concepts

decimal conversion

When converting decimals to percentages, it's important to first understand what a decimal represents. Decimals are a way to express fractions or parts of a whole number using the base-10 system. For example, the decimal 0.75 represents 75 out of 100, or 75%.

To convert a decimal to a percentage, the fundamental approach involves multiplying the decimal number by 100. This operation moves the decimal point two places to the right. For instance, converting 0.3 to a percentage involves calculating: ewline ewline \(0.3 \times 100 = 30\).

Therefore, 0.3 as a percentage is 30%. This simple multiplication is the core process of decimal conversion.

percentage calculation

Calculating percentages is a vital skill in mathematics and everyday life. When converting a decimal to a percentage, the primary calculation you need is to multiply by 100. This effectively changes the decimal fraction into a more understandable percentage form.

Let's take another example: converting 0.45 to a percentage. The step-by-step process looks like this:

• Step 1: Identify the decimal (e.g., 0.45).
• Step 2: Multiply the decimal number by 100 to change it into a percentage: ewline \(0.45 \times 100 = 45\).
• Step 3: Append the percentage symbol. Thus, 0.45 equals 45%.

Always remember that multiplying any decimal by 100 converts it into a percentage, making this calculation simple and efficient.

basic arithmetic

Basic arithmetic is the foundation upon which complex mathematics is built. It includes fundamental operations such as addition, subtraction, multiplication, and division. For decimal to percentage conversions, multiplication is the key operation needed.

Let's break down the arithmetic behind multiplying a decimal by 100. For instance, given a decimal like 3:

• Step 1: Understand that 3 is actually 3.0, which can be treated as a decimal.
• Step 2: Set up the multiplication operation meaning ewline \(3 \times 100\).
• Step 3: Execute the multiplication leading to ewline \(3 \times 100 = 300\).
• Step 4: The result 300 is the percentage form, equal to 300%.

Mastering these basic arithmetic steps ensures that decimal to percentage conversion, among other mathematical tasks, becomes an easy and straightforward process.