0.06% of 250% of 1600 is equal to how much?

Introduction / Context:
This question is about handling nested percentages correctly. It asks the value of 0.06% of 250% of 1600, which involves working with both percentage values and their decimal equivalents. It tests careful handling of small percentages and multiple stages of percentage application.

Given Data / Assumptions:

• We need to compute 250% of 1600 first.
• Then we must take 0.06% of that result.
• All percentage operations follow the standard definition: x% = x/100.

Concept / Approach:
The standard approach is to convert each percentage to its decimal form. 250% becomes 2.5 and 0.06% becomes 0.0006. We first multiply 2.5 by 1600 to get an intermediate value, and then multiply that result by 0.0006. Since multiplication is associative, we can also combine the percentages first and then apply to 1600, but doing it step by step is clearer.

Step-by-Step Solution:
Step 1: Convert 250% to decimal: 250% = 250/100 = 2.5. Step 2: Compute 250% of 1600: 2.5 * 1600 = 4000. Step 3: Convert 0.06% to decimal: 0.06% = 0.06/100 = 0.0006. Step 4: Compute 0.06% of the previous result: 0.0006 * 4000. Step 5: 0.0006 * 4000 = 2.4. Step 6: Therefore, the required value is 2.4.

Verification / Alternative check:
We can also combine the operations algebraically. The expression is (0.06/100) * (250/100) * 1600. Compute the combined fraction: (0.06 * 250) / 10000 = 15 / 10000 = 0.0015. Then 0.0015 * 1600 = 2.4. This matches the earlier result and confirms the answer.

Why Other Options Are Wrong:

• 24: This is ten times the correct answer, possibly from treating 0.06% as 0.06 instead of 0.0006.
• 0.24: This is a factor of ten smaller than 2.4 and could come from one misplaced decimal.
• 0.024: This is two decimal places off and indicates confusion in handling the percent conversion.
• 4.8: This may arise from doubling 2.4 by mistake.

Common Pitfalls:
Students often handle very small percentages like 0.06% incorrectly by converting them to 0.06 instead of 0.0006. Another common issue is not maintaining enough care with decimal places, leading to answers off by factors of ten or hundred. Writing each conversion step explicitly as division by 100, and checking the order of magnitude at the end, helps avoid these errors.

Final Answer:
The value of 0.06% of 250% of 1600 is 2.4.