Find the value of 0.09% of 25% of 1200, that is, first take 25% of 1200 and then find 0.09% of that result.

Introduction / Context:
This question tests your understanding of nested percentages, where one percentage is taken of another percentage of a base number. It is a straightforward numerical computation but requires careful handling of decimal forms of percentages to avoid calculation errors.

Given Data / Assumptions:

• We need to compute 0.09 percent of 25 percent of 1200.
• Base number = 1200.
• First percentage = 25 percent.
• Second percentage = 0.09 percent.
• All operations are standard percentage calculations with no rounding specified.

Concept / Approach:
Percentages can be converted into decimal multipliers. 25 percent = 25 / 100 = 0.25. 0.09 percent = 0.09 / 100 = 0.0009. The required value is: Result = 0.09 percent * (25 percent of 1200). This can be written as: Result = 0.0009 * 0.25 * 1200.

Step-by-Step Solution:
Step 1: Convert 25 percent to decimal: 25 percent = 0.25. Step 2: Find 25 percent of 1200: 0.25 * 1200 = 300. Step 3: Convert 0.09 percent to decimal: 0.09 percent = 0.0009. Step 4: Compute 0.09 percent of 300: 0.0009 * 300. Step 5: Multiply 0.0009 * 300 = 0.27.

Verification / Alternative check:
Instead of doing the steps separately, we can combine all factors at once. Result = (0.09 / 100) * (25 / 100) * 1200 = (0.09 * 25 * 1200) / 10,000. Compute the numerator: 0.09 * 25 = 2.25, then 2.25 * 1200 = 2700. Now 2700 / 10,000 = 0.27. This alternate approach gives the same result and confirms the accuracy of the calculation.

Why Other Options Are Wrong:
2.7: This is ten times larger than the correct answer and arises if the decimal place is misplaced. 27 and 270: These are huge compared with the fractions of a percent being applied and indicate that percentages were not converted properly. 0.027: This is one tenth of the correct value and may result from incorrectly treating one of the percentages as a plain decimal rather than a percent.

Common Pitfalls:
Students often forget that a percent itself needs to be divided by 100, and when two percentages are multiplied, the effect is divided by 10,000. Misplacing decimal points is very common in such questions. The safest approach is to convert each percentage step by step into a decimal and multiply carefully, or to carry out the entire calculation as a fraction over 10,000.

Final Answer:
The value of 0.09 percent of 25 percent of 1200 is 0.27.