Question

Write each percent as a decimal number. $$100.5 \%$$

Short answer

Answer: 1.005

Step-by-step solution

Identify the given percentage

The given percentage is $$100.5 \%$$.

Divide the percentage by 100

To convert the percentage into a decimal, divide the given percentage by 100: $$\frac{100.5}{100}$$.

Simplify the expression

Simplify the expression: $$\frac{100.5}{100} = 1.005$$.

Write the decimal number

The decimal number equivalent to $$100.5 \%$$ is $$1.005$$.

Key concepts

Percentage Conversion

Converting a percentage to a decimal is a fundamental concept in mathematics. It is often used in everyday situations, such as calculating discounts or determining statistics. To convert a percentage to a decimal, consider the percentage value as being out of 100. This means you need to divide the percentage by 100. For example, with a percentage like 100.5%, you would perform the operation \( \frac{100.5}{100} \). This division process is at the heart of percentage conversion and helps in accurately translating percentage figures into decimal form.

Decimal Representation

Decimal representation is essentially another way to express fractions or percentages. When you convert percentages into decimals, you make the values easier to work with, especially in calculations. For instance, the percentage 100.5% becomes 1.005 in decimal form. This means that for every 100 parts, there are 100.5 parts, simplifying this to a scale where you have 1.005 parts for every one part, or unit. Decimals provide a clean and concise way to depict values less than, equal to, or greater than a whole number, making them highly useful in both mathematics and real-life applications.

Basic Arithmetic

Basic arithmetic operations, like addition, subtraction, multiplication, and division, are key when working with percentages and decimals. In our task of converting percentages to decimals, division is the primary operation. You take the percentage figure—such as 100.5%—and divide by 100, resulting in 1.005. This practice strengthens your ability to manipulate and understand numerical data. Arithmetic ensures that numbers are handled accurately, supporting further math endeavors such as solving equations or analyzing graphs and data.

Mathematics Education

Understanding percentages and their conversion to decimals is crucial in mathematics education. It forms a building block for more complex mathematical concepts. Students encounter percentages in numerous subjects, including science, economics, and statistics. This exercise of converting percentages to decimals not only sharpens math skills but also provides a practical tool for interpreting numerical information accurately. By mastering these basics, students equip themselves with the fundamental skills needed to navigate through more advanced mathematical topics and real-world scenarios where quantitative analysis is paramount.