Problem 8 - Prealgebra

Question

Solve each of the following problems. What number is \(2 \%\) of \(49 ?\)

Step-by-Step Solution

Answer

2% of 49 is 0.98.

Step 1: Understand the Problem

To find what number is 2% of 49, we need to convert the percentage into a decimal and multiply it by 49. Basically, we're trying to calculate 2% of the given number, 49.

Step 2: Convert Percentage to Decimal

To convert a percentage into a decimal, divide by 100. For 2%, this means \( \frac{2}{100} = 0.02 \).

Step 3: Multiply by the Given Number

Now take the decimal representation of the percentage (0.02) and multiply it by 49, as follows: \( 0.02 \times 49 \).

Step 4: Perform the Multiplication

Carry out the multiplication: \( 0.02 \times 49 = 0.98 \).

Step 5: Interpret the Result

The result of the multiplication gives us the number that is 2% of 49. Thus, 0.98 is our answer.

Key Concepts

Percent to Decimal Conversion

Many students start stumbling on percentage problems due to misunderstandings about percentages. It's simple once you grasp how to convert a percentage to a decimal. A percentage is a part-out-of-a-whole representation where the whole is 100. So, to convert a percentage to a decimal, divide by 100.
This is because percentages represent parts per hundred.
For instance, to convert 2% to a decimal:

• Breakdown 2% to its basic form: 2 parts out of 100
• Perform the division: \(\frac{2}{100} = 0.02\)

Once the division is completed, you have your decimal form. Remember, this conversion is fundamental to tackling percentage problems.

Multiplication of Decimals

Once you have your decimal, the next crucial step is multiplying decimals, which is simpler than it sounds. Suppose you have to multiply 0.02 by 49 to find what 2% of 49 is. Follow these steps:

• Ignore the decimals initially and multiply as if they were integers. Here, you multiply 2 by 49.
• Calculate: \(2 \times 49 = 98\)
• Now, count the total number of decimal places in the multiplier (0.02) and the multiplicand (49 has no decimal). The decimal part of 0.02 has two decimal places, so your result must also have two decimal places.
• Thus, place the decimal point in 98 two places from the right, making it 0.98.

Through this process, you find that 0.02 multiplied by 49 is 0.98, which is 2% of 49.

Problem-Solving Steps

Breaking down a problem into bite-sized steps is critical for solving math problems efficiently. Let’s review how we solved the problem 'What is 2% of 49?' through clear problem-solving steps:

• **Understand the problem**: You’re finding a small part (2%) of a whole (49).
• **Convert the percentage to a decimal**: We converted 2% to 0.02.
• **Multiply the decimal by the whole number**: Compute \(0.02 \times 49\).
• **Perform the multiplication**: This gave us 0.98.
• **Interpret the result**: Conclude that 0.98 is indeed 2% of 49.

By following these structured steps, you can systematically solve similar percentage problems with ease.

Basic Arithmetic Operations

Understanding and mastering basic arithmetic operations is crucial. Operations like multiplication and division underpin most percentage problem solutions. So, let's recap:

• **Multiplication**: When multiplying a decimal by a number, treat them as integers first, and adjust the decimal places in the result later.
• **Division**: Used when converting percentages to decimals. Divide the percentage value by 100 to get a decimal.

These basic operations are foundational. Even more, they enable success in more complex math and real-world applications. So, becoming comfortable with them is both practical and essential for future learning.