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Chapter 7: Problem 55

In a survey of high school students, \(28 \%\) said they volunteered at least 2 hours a week. In a class of 32 high school students, how many would you predict volunteer at least 2 hours a week? (Lesson \(6-10\) )

Short Answer

Expert verified
Approximately 9 students volunteer at least 2 hours a week.

Step by step solution

01

Understanding the Problem

We need to find out how many students, out of a total of 32, volunteer at least 2 hours a week, given that 28% of them do so according to a survey.
02

Convert Percentage to Decimal

Convert the percentage of students who volunteer into a decimal for calculation purposes. Since 28% is given, we convert this to decimal by dividing by 100: \(28\% = 0.28\).
03

Calculate the Number of Students

Use the decimal to find the number of students who volunteer. Multiply the total number of students (32) by the decimal \(0.28\): \[32 \times 0.28 = 8.96\].
04

Round to the Nearest Whole Number

Since the number of students must be a whole number, round the result of 8.96 to the nearest whole number, which is 9.

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Key Concepts

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

Understanding Surveys
Surveys are essential tools used to collect data from a specific group of people. They are often conducted to understand opinions, behaviors, or characteristics within a population.
When a survey indicates that a percentage of respondents have a certain trait or behavior, it provides a snapshot of broader trends. Such data helps in making predictions about a larger group.
  • A survey result, like the 28% in our example, indicates a portion of respondents. Here, it shows how many high school students participate in volunteering.
  • Surveys can be conducted through various methods, such as questionnaires or interviews.
  • They can cover different population sizes, from a small class to a nationwide study.
Converting Percentages to Decimals
Converting percentages to decimals is a fundamental math skill, essential for various calculations.
To convert a percentage to a decimal, you divide the percentage by 100. This step is vital for accurate calculations.
  • For instance, to convert 28% to a decimal: divide by 100. Thus, 28% becomes 0.28.
  • This conversion is straightforward but necessary for multiplying percentages with other numbers.
  • Decimals are versatile; they are easier to work within mathematical equations.
Multiplication with Decimals
Multiplying with decimals allows us to predict outcomes based on percentage data, like the survey example.
Once a percentage is converted to a decimal, it can be used to multiply other numbers.
  • In the example, the number of students (32) is multiplied by the decimal (0.28): \(32 \times 0.28 = 8.96\).
  • This product (8.96) approximates how many students, out of 32, volunteered.
  • Multiplication with decimals demands attention to detail, as it affects the accuracy of predictions.
  • Finally, results often need to be rounded to a whole number, as in our exercise where 8.96 rounds to 9.

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