Twenty five percent of twenty five percent of a quantity is equal to which decimal value?

Introduction / Context:
This is a simple percentage and decimal conversion question. It asks you to compute a percentage of another percentage and then express the final result in decimal form. Such questions test basic understanding of how percentages convert to decimals and how to multiply them correctly without confusion.

Given Data / Assumptions:

• We are given 25 percent of 25 percent of some quantity.
• No actual base quantity is specified, so we can use a convenient assumed value if needed.
• The final answer must be expressed as a decimal number.

Concept / Approach:
Percent means per hundred. So 25 percent is 25/100 or 0.25 in decimal form. To find 25 percent of 25 percent, we multiply 0.25 by 0.25. It does not matter what the original quantity is, because we are only asked for the fraction of that quantity in decimal form. When two percentages are applied successively to the same base, you simply multiply their decimal representations.

Step-by-Step Solution:
Step 1: Convert 25 percent to decimal: 25 percent = 25/100 = 0.25.Step 2: Compute 25 percent of 25 percent as 0.25 * 0.25.Step 3: Multiply 0.25 by 0.25 to get 0.0625.Step 4: Therefore, 25 percent of 25 percent of any quantity is equal to 0.0625 times that quantity.

Verification / Alternative check:
As a check, assume the base quantity is 1. Then 25 percent of 1 is 0.25. Now take 25 percent of 0.25, which is 0.25 * 0.25 = 0.0625. This matches our calculation. If we took a different base, say 100, then 25 percent of 100 is 25, and 25 percent of 25 is 6.25. As a fraction of 100, 6.25 is still 0.0625, so the value is consistent.

Why Other Options Are Wrong:
The value 0.0210 corresponds to 2.1 percent, which is smaller than 6.25 percent and does not match the multiplication of 0.25 by 0.25. The value 0.03145 is an arbitrary decimal with no relation to the simple product of 0.25 and 0.25. The value 0.3210 would be 32.1 percent, much larger than expected. The value 0.2500 would represent just 25 percent, not 25 percent of 25 percent. Only 0.0625 is correct.

Common Pitfalls:
A common mistake is to add percentages instead of multiplying them, for example taking 25 percent of 25 percent as 50 percent or 0.5, which is incorrect. Another error is to misplace decimal points when converting percentages to decimals, such as writing 25 percent as 0.025. Remember that to convert a percentage to a decimal, you divide by 100, and to apply one percentage after another, you multiply their decimal values.

Final Answer:
The decimal value corresponding to 25 percent of 25 percent is 0.0625, so the correct option is 0.0625.