Problem 100 - Algebra A Combined Function

Question

Which of the following are correct? a. \(0.231=23.1 \%\) b. \(5.12=0.0512 \%\) c. \(3.2=320 \%\) d. \(0.0175=0.175 \%\)

Step-by-Step Solution

Answer

Options a and c are correct.

Step 1: Convert Percentages to Decimals for each Option

To check if the statements are correct, convert each percentage given in the options back into a decimal and compare with the original number.- For option a, convert 23.1% to a decimal: 23.1% = \( \frac{23.1}{100} = 0.231 \)- For option b, convert 0.0512% to a decimal: 0.0512% = \( \frac{0.0512}{100} = 0.000512 \)- For option c, convert 320% to a decimal: 320% = \( \frac{320}{100} = 3.2 \)- For option d, convert 0.175% to a decimal: 0.175% = \( \frac{0.175}{100} = 0.00175 \)

Step 2: Compare Converted Decimals with Given Decimals in Problem

Now, compare each decimal obtained from the conversion with the given number in the problem: - For option a: The obtained decimal 0.231 matches the given number 0.231. So, this option is correct. - For option b: The obtained decimal 0.000512 does not match the given number 5.12. So, this option is incorrect. - For option c: The obtained decimal 3.2 matches the given number 3.2. So, this option is correct. - For option d: The obtained decimal 0.00175 does not match the given number 0.0175. So, this option is incorrect.

Step 3: Identify Correct Statements

List the options that are correctly matched based on the above comparisons: - Option a: Correct. - Option b: Incorrect. - Option c: Correct. - Option d: Incorrect.

Key Concepts

Understanding Decimal Conversions

Decimal conversions are crucial in mathematics, as they help you switch between percentages and their decimal forms effortlessly. When you see a percentage, remember that it's a way of expressing a number as a fraction of 100. For example, 23.1% can be converted into its decimal form by dividing by 100. This action effectively moves the decimal point two places to the left. Thus, 23.1% becomes 0.231.
If you're working with very small percentages like 0.0512%, the same rule applies. Divide 0.0512 by 100, resulting in the decimal 0.000512. This shows how even a small percentage translates into a tiny decimal. Remember that understanding these conversions helps immensely when it's time to tackle various percentage problems.

Mastering Math Problem Solving

Approaching math problems can sometimes feel daunting, but breaking them down step by step makes them much more manageable. Let's take the exercise of checking whether given statements involving percentages and decimals are correct.
The first step involves converting the percentage into its decimal form by dividing by 100. Once you have the decimal forms, the next challenge is a comparison. Compare these converted decimals against the given numbers in the problem to confirm their correctness.
To further ensure accuracy, make it a habit to:

• Read the problem carefully before starting.
• Perform one step at a time.
• Always double-check your work for mistakes.

Using these steps can transform a seemingly complicated problem into a straightforward task. The more you practice, the more naturally these steps will come to you.

Step-by-Step Math Solutions Simplified

Let's simplify step-by-step math solutions to verify accuracy in exercises. With percentage conversion problems, follow a clear sequence for best results.
Begin with the percentage, and convert it to a decimal by dividing by 100, as detailed earlier. With the decimal now in hand, compare it to the original number given in the statement. If they match, the statement is correct. Otherwise, it's incorrect.

• First, address one option at a time to avoid confusion.
• Write down each step clearly to keep your work organized.
• Verify your results before concluding.

By sticking to a detailed strategy, errors are minimized and understanding improves. This approach not only brings clarity but also boosts confidence in solving complex math problems efficiently.