Question

In 1 hour there are 3600 seconds. By what conversion \(\mathrm{fac}-\) tor would you multiply 250 seconds to convert it to hours? By what conversion factor would you multiply 3.84 hours to convert it to seconds?

Short answer

To convert 250 seconds to hours, multiply by \( \frac{1}{3600} \). To convert 3.84 hours to seconds, multiply by 3600.

Step-by-step solution

Finding the Conversion Factor from Seconds to Hours

To find the conversion factor from seconds to hours, we will use the information that 1 hour is equal to 3600 seconds. We want to know how many hours are in 250 seconds. The conversion factor is obtained by taking the ratio of 1 hour to 3600 seconds.

Using the Conversion Factor to Convert Seconds to Hours

To convert 250 seconds to hours, we multiply 250 by the conversion factor. The conversion factor from seconds to hours is \( \frac{1 \text{ hour}}{3600 \text{ seconds}} \) Therefore, \( 250 \text{ seconds} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \) gives us the time in hours.

Finding the Conversion Factor from Hours to Seconds

To find the conversion factor from hours to seconds, we reverse the relationship used for seconds to hours. Because 1 hour is equal to 3600 seconds, the conversion factor from hours to seconds is simply 3600.

Using the Conversion Factor to Convert Hours to Seconds

To convert 3.84 hours to seconds, we multiply 3.84 by the conversion factor of 3600. So, \( 3.84 \text{ hours} \times 3600 \text{ seconds/hour} \) will give us the total seconds.

Key concepts

Seconds to Hours Conversion

Understanding how to convert seconds to hours is a fundamental skill in time calculation. It lets you easily switch between these two units of time based on your needs, whether you're timing an experiment or logging hours for work.

Let's begin with the basics: there are 3600 seconds in one hour. If you have a certain number of seconds and you want to find out how many hours that represents, you divide by 3600. This number, 3600, is the conversion factor, and it’s a key component in time conversions. You’re essentially determining how many sets of 3600 seconds you have in your total count of seconds.

For example, using the information from the exercise, to convert 250 seconds to hours, you multiply 250 seconds by the conversion factor, which in this case is the ratio \( \frac{1 \text{ hour}}{3600 \text{ seconds}} \). When you do the math, \( 250 \text{ seconds} \times \frac{1 \text{ hour}}{3600 \text{ seconds}} \) simplifies to approximately 0.06944 hours. This conversion factor method is quick, efficient, and can be applied to any quantity of seconds you wish to convert into hours.

Units of Time

Units of time range from the smallest, like milliseconds, up to seconds, minutes, hours, and extend to days, years, and even millennia. Each unit provides a different scale to measure time, suitable for various contexts. Knowing how to convert between these units is incredibly useful.

To keep everything straight, remember that conversions within time units are always based on standard, fixed amounts. For seconds to minutes and minutes to hours, the magic numbers are 60 and 60, respectively. One minute is 60 seconds, and one hour is 60 minutes, or 3600 seconds. The more comfortable you are with these fundamental relationships, the easier it will be to navigate between units for any time-related calculation.

Continuity is crucial when working with units of time, ensuring accuracy and preventing confusion. Always make sure to double-check your conversions, especially when dealing with units different from your usual reference frame, for instance, converting days into seconds or weeks into minutes.

Time Calculation

Time calculation involves using these conversion factors to switch between units or to find the sum, difference, and other operations involving time. It’s crucial to make accurate calculations for scheduling, scientific experiments, tracking workouts, and more.

Simple multiplication and division can be your first steps. As shown in the solutions, to convert hours to seconds, you would multiply by the number of seconds in one hour (3600). In our example, converting 3.84 hours to seconds involves multiplying 3.84 by 3600, which equals 13824 seconds.

It's not just about converting; you can also add and subtract time values once they are in the same units to find durations or differences. Time calculation is rooted in these basic principles, and mastering them will solve most everyday problems you'll encounter with regard to time management and measurement.