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Chapter 2: Problem 56

Solve. What is \(40 \%\) of \(2 ?\)

Short Answer

Expert verified
0.80

Step by step solution

01

- Convert Percentage to Decimal

First, convert the percentage to a decimal. Since 40% means 40 out of 100, divide 40 by 100: \[ 40\text{ %} = \frac{40}{100} = 0.40 \]
02

- Multiply by the Given Number

Next, multiply the decimal form of the percentage by the number you are finding the percentage of. Here, that number is 2: \[ 0.40 \times 2 = 0.80 \]
03

- Write the Final Answer

The result from the previous step is the answer to the question. Thus, 40% of 2 is 0.80.

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Key Concepts

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

Convert Percentage to Decimal
Percentages represent parts per hundred. When you want to convert a percentage to a decimal, you divide by 100. It's like saying, 'What fraction of 100 is this number?' For example, if you have 40%, you divide 40 by 100: \( \text{ 40% } = \frac{\text{40}}{\text{100}} = \text{0.40} \).
Breaking it down:
  • Remove the percentage symbol (\text{%}).
  • Move the decimal point two places to the left or simply divide by 100.
Following these steps, 40% becomes 0.40. This conversion is crucial because it's easier to use decimals in calculations.
With decimals, you can seamlessly perform various arithmetic operations.
Multiplication with Percentage
After converting the percentage to a decimal, the next step is to multiply it by the given number. Multiplication allows you to find the actual value represented by the percentage.
For example, you have 0.40 (which is 40%) and you need to find 40% of 2. Multiply 0.40 by 2: \ You set up the operation as:
  • \(0.40 \times 2 \)
This yields \( \text{ 0.80} \). Breakdown:
  1. Multiply the decimal form of the percentage by the given number.
  2. Count the number of decimal places in the factors (0.40 has two).
  3. Ensure your result reflects the correct placement of the decimal.
 Multiplication with percentages is essentially finding a fraction of a number. In this case, multiplying 0.40 by 2 gives you 0.80, which is 40% of 2.
Basic Arithmetic Operations
Understanding basic arithmetic operations is essential for solving percentage problems. It helps you to seamlessly convert and multiply without confusion. There are four main operations: addition, subtraction, multiplication, and division. For percentage problems, you often focus on:
  • Multiplication: to find a part of a whole.
  • Division: to convert percentages to decimals.
In our example, we perform multiplication. We convert 40% to 0.40 and multiply by the number 2. It's important to be accurate with decimal placement in your calculations.
Practicing these operations ensures that you can handle more complex problems effortlessly. Remember, mathematics is built on these fundamental principles!

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