How to Express 8 Hours as a Percentage of 2 Days

A very common mistake students make in percentage problems is trying to calculate the numbers while they are in different units (like dividing hours by days). The golden rule of math is: You can only compare quantities if their units are exactly the same.

Question (Click to Flip)

What if the question was 12 hours as a percentage of 1 day?

Answer

1 day = 24 hours. The fraction is 12/24, which simplifies to 1/2. Multiply by 100, and the answer is exactly 50%.

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Key Facts

Always convert the bigger unit to the smaller unit (e.g., convert Kg to Grams, or Km to Meters) to avoid dealing with confusing decimal numbers during division.

1. Step 1: Convert to the Same Unit

We have two quantities: '8 hours' and '2 days'.
We must convert the larger unit (Days) into the smaller unit (Hours) to make the math easy.
We know that 1 Day = 24 Hours.
Therefore, 2 Days = 2 × 24 = 48 Hours.
Now, the question becomes much simpler: Express 8 hours as a percentage of 48 hours.

2. Step 2: Set up the Fraction

To find the percentage, we write the required quantity as a fraction of the total quantity.
Fraction = $\frac{\text{Required Time}}{\text{Total Time}}$
Fraction = $\frac{8}{48}$

3. Step 3: Multiply by 100

To convert any fraction into a percentage, you simply multiply it by 100.
Percentage = $\left( \frac{8}{48} \right) \times 100$
Let's simplify the fraction first: Both 8 and 48 are divisible by 8. So, $8/48$ becomes $1/6$.
Percentage = $\frac{1}{6} \times 100 = \frac{100}{6}$
Dividing 100 by 6 gives us 16.66% (or $16\frac{2}{3}%$).

4. Final Answer

8 hours is exactly 16.66% of 2 days.

Questions and Answers

What if the question was 12 hours as a percentage of 1 day?+

1 day = 24 hours. The fraction is 12/24, which simplifies to 1/2. Multiply by 100, and the answer is exactly 50%.

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