Solve each problem using dimensional analysis. evey number must have a unit. work must be shown.

Question

ten thousand hours (10,000 hrs) is equal to how many days?

Answer 1

To convert hours to days using dimensional analysis, we start with the relationship between hours and days.

1 day = 24 hours

Now, we can set up the conversion using this relationship:

\[ 10,000 \text{ hrs} \times \frac{1 \text{ day}}{24 \text{ hrs}} \]

Notice that the hours unit in the numerator will cancel with the hours unit in the denominator:

\[ = 10,000 \times \frac{1}{24} \text{ days} \]

Now, we perform the calculation:

\[ = \frac{10,000}{24} \text{ days} \]

Calculating the division:

\[ = 416.6667 \text{ days} \]

So, rounded to the nearest whole number, we can say:

\[ 10,000 \text{ hrs} \approx 417 \text{ days} \]

Thus, 10,000 hours is equal to approximately 417 days.