What percentage of a day is equal to 3 hours?

Introduction / Context:
This question tests a basic understanding of percentages and time. A day has 24 hours, and we are asked to find what percentage 3 hours represents out of a full day. This is a simple ratio to percentage conversion and is commonly used in time management and scheduling problems.

Given Data / Assumptions:

• 1 full day = 24 hours.
• We are given a time interval of 3 hours.
• We must express 3 hours as a percentage of 24 hours.

Concept / Approach:
To find what percentage one quantity is of another, we use the formula: Percentage = (Part / Whole) * 100. Here, the part is 3 hours and the whole is 24 hours. Once we find 3 / 24, we multiply by 100 to get the percentage. It is often useful to simplify the fraction before multiplying to reduce the chance of errors.

Step-by-Step Solution:
Step 1: Identify the part and the whole. Part = 3 hours, Whole = 24 hours. Step 2: Form the fraction representing the part of the whole: 3 / 24. Step 3: Simplify 3 / 24 by dividing numerator and denominator by 3 to get 1 / 8. Step 4: Convert the fraction to a percentage: (1 / 8) * 100. Step 5: Compute 1 / 8 = 0.125. Step 6: Multiply by 100: 0.125 * 100 = 12.5. Step 7: Therefore, 3 hours is 12.5% of a 24 hour day.

Verification / Alternative check:
We can also think of a day as divided into eight equal parts of 3 hours each (since 24 / 3 = 8). Each equal part must then correspond to one eighth of the day. As a percentage, one eighth is 12.5%, confirming our calculation that 3 hours is exactly 12.5% of a full day.

Why Other Options Are Wrong:
14.9%, 15.6%, 11.4%, and 10% all represent different fractions of a day. For example, 10% of a day would be 2.4 hours, not 3 hours. 15.6% would be more than 3 hours. None of these match the exact fraction 1 / 8 which corresponds to 3 out of 24 hours. Only 12.5% is equivalent to 3 / 24 of the day.

Common Pitfalls:
Some learners mistakenly divide 24 by 3 instead of forming the ratio 3 / 24, or they calculate the decimal fraction but forget to multiply by 100 to convert to percentage. Others may confuse the base, for example taking 3 as the whole and 24 as the part. Always remember that the percentage is relative to the whole quantity, which in this case is 24 hours.

Final Answer:
3 hours is 12.5% of a day.