Question

Write two conversion factors (two different ratios) to express the fact that there are \(24 \mathrm{~h}\) in a day.

Short answer

The two conversion factors to express 24 hours in a day are: 1) \(\frac{24 \text{ hours}}{1 \text{ day}}\) 2) \(\frac{1 \text{ day}}{24 \text{ hours}}\)

Step-by-step solution

Conversion Factor 1: Hours to Days

To convert from hours to days, we can write a ratio that includes 24 hours (the number of hours in a day) and the corresponding value for days, which is 1 day. Therefore, the first conversion factor is: \[\frac{24 \text{ hours}}{1 \text{ day}}\]

Conversion Factor 2: Days to Hours

To convert from days to hours, let's create another ratio, this time with 1 day in the numerator and the corresponding value for hours (24 hours) in the denominator. The second conversion factor is: \[\frac{1 \text{ day}}{24 \text{ hours}}\] These two conversion factors can be used to convert between hours and days in various problems, depending on the unit required by the solution.