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Chapter 4: Problem 3

Convert each of the following percents to a decimal. $$ 2.5 \% $$

Short Answer

Expert verified
Answer: The decimal representation of $$2.5 \%$$ is 0.025.

Step by step solution

01

Identify the given percentage

The percentage given in this exercise is $$2.5 \%$$.
02

Divide the percentage by 100

To convert the percentage to a decimal, simply divide it by 100. So, $$ \frac{2.5}{100} $$
03

Perform the division

After dividing the percentage by 100, we get $$ \frac{2.5}{100} = 0.025 $$
04

Write the result as a decimal number

Finally, we can express the result as a decimal number: $$ 2.5 \% = 0.025 $$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Percentage
A percentage is a way to express a number as a part of a whole. It represents how many parts of 100 something is. For example, when we say 2.5%, we mean 2.5 out of 100. This is a handy way to compare proportions quickly.
Understanding percentages is important in everyday life. We use them in shopping for discounts, calculating interest rates, or comparing statistics.
  • Percent means "per hundred."
  • The symbol \(\%\) is used to represent percent.
    • To grasp it easily, always think of a whole as divided into 100 equal parts. This makes understanding fractions and decimals much easier.
    Mathematical Division in Conversion
    When converting percentages to decimals, we often use mathematical division. The divider here is 100, since percentages are parts of 100. The exercise we're looking at requires us to divide 2.5 by 100.
    This step is crucial because dividing by 100 shifts the decimal point two places to the left. Here's how it works:
  • When you have a percentage like 2.5%, think of it as 2.5 out of 100.
  • Divide 2.5 by 100, which mathematically means using the operation \( \frac{2.5}{100} \).

    • Once divided, you move the decimal point two places to the left, resulting in 0.025. This method works on any percentage, not just 2.5%. Recall that:
  • Every percentage when divided by 100 changes form from percentage to decimal.
    • Practical Application in Grade 7 Math
    In Grade 7 Math, decimals and percentages are pivotal. It's a stage where students strengthen their understanding of numbers, especially when working with fractions, decimals, and percentages. Converting among these forms sharpens numerical reasoning.
    Why is it so significant? Because it builds a foundation for more complex math later on. For example, students will start learning how to:
  • Work with ratios and proportions.
  • Understand real-world math problems involving percentages like discounts or probability.
  • Transition between different forms of numbers with ease.

    • This groundwork in Grade 7 ensures that as students progress, they face fewer hurdles with more complex mathematics. Encouraging students to see the connection between math problems and real-world applications fosters a deeper interest and appreciation for math.

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    Most popular questions from this chapter

    Convert each of the following decimals to a percent. $$ 1.246 $$

    Convert each of the following fractions to a percent. $$ \frac{2}{5} $$

    Convert each of the following decimals to a percent. $$ 0.06 $$

    Answer the following questions about percents. $$ \text { What is } 30 \% \text { of } 520 \text { ? } $$

    Answer the following questions about percents. $$ \text { What is } 28 \% \text { of } 10 ? $$
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