Problem 39 - Introductory Chemistry Atoms First

Question

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

Step-by-Step Solution

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 1: 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: \[\frac{24 \text{ hours}}{1 \text{ day}}\]

Step 2: 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.

Key Concepts

hours to days conversion

When thinking about converting hours to days, it's all about understanding the relationship between the two units. We know that 24 hours is equal to 1 day. So, whenever we're given a number of hours and we need to find out how many days that equals, we use this as our conversion ratio. The conversion factor comes from the equation:

• 1 day = 24 hours

This can be expressed as a ratio that helps in conversion:

• \(\frac{24 \text{ hours}}{1 \text{ day}}\)

To convert hours into days, you divide the number of hours by 24. For example, if you have 48 hours, you divide by 24, resulting in 2 days. This is a direct use of the conversion factor, helping to smoothly transition from a smaller unit of time to a larger one.

days to hours conversion

Now, let's look at converting from days to hours. The process is like a mirror image of converting hours to days. Since 1 day equals 24 hours, this is our fundamental relationship. To express this conversion, we use the opposite ratio:

• \(\frac{1 \text{ day}}{24 \text{ hours}}\)

With this factor, converting from days to hours involves multiplication rather than division. Say you have 2 days and need to know how many hours that is. Simply multiply 2 days by 24 hours per day, giving you 48 hours. This conversion factor is particularly useful when larger time units need to be understood in finer detail or smaller amounts like hours.

ratio in unit conversion

Understanding ratios is a crucial aspect of unit conversion. Ratios allow us to express the relationship between two quantities, which in this case are hours and days. A ratio is a comparison, and it can be written in a form that makes converting between units easy. The two important ratios derived from the relationship "24 hours equals 1 day" are:

• \(\frac{24 \text{ hours}}{1 \text{ day}}\)
• \(\frac{1 \text{ day}}{24 \text{ hours}}\)

These ratios are simple expressions, yet powerful tools in calculations. They help you switch back and forth between units without confusion. By applying the appropriate ratio, you ensure the correct conversion, maintain consistency in units, and eliminate errors in calculations. Next time you encounter a unit conversion problem, remember that the ratio is your friend!