What fraction of an hour is 900 seconds using dimensional analysis
The Correct Answer and Explanation is:
To find what fraction of an hour 900 seconds represents using dimensional analysis, follow this step-by-step method:
Step-by-step Calculation:
- Start with what is given:
We are given 900 seconds. - Convert seconds to minutes:
There are 60 seconds in 1 minute, so: 900 seconds×1 minute60 seconds=15 minutes900\ \text{seconds} \times \frac{1\ \text{minute}}{60\ \text{seconds}} = 15\ \text{minutes}900 seconds×60 seconds1 minute=15 minutes - Convert minutes to hours:
There are 60 minutes in 1 hour, so: 15 minutes×1 hour60 minutes=1560 hours=14 hour15\ \text{minutes} \times \frac{1\ \text{hour}}{60\ \text{minutes}} = \frac{15}{60}\ \text{hours} = \frac{1}{4}\ \text{hour}15 minutes×60 minutes1 hour=6015 hours=41 hour
Thus, 900 seconds is equal to 1/4 of an hour.
Explanation
Dimensional analysis is a powerful tool in science and mathematics used to convert one unit of measurement to another. It ensures that units are consistently treated throughout a calculation, which helps avoid errors. In this case, we are asked to find what fraction of an hour 900 seconds represents.
We begin with the quantity we are given, which is 900 seconds. The goal is to convert seconds into hours. To do this, we use known conversion factors. The first step is to convert seconds into minutes. Since 1 minute is equal to 60 seconds, we set up a conversion factor that allows the units of seconds to cancel out. By multiplying 900 seconds by the fraction 1 minute over 60 seconds, we cancel out the seconds and are left with minutes. The calculation results in 15 minutes.
The next step is to convert minutes into hours. Again, we use a known conversion factor: 1 hour equals 60 minutes. We multiply 15 minutes by the fraction 1 hour over 60 minutes. This cancels out the minutes and leaves us with hours. Doing the math, we get 15 over 60, which simplifies to 1 over 4.
So, through dimensional analysis, we determined that 900 seconds is equivalent to one fourth of an hour. Each step followed logical reasoning and unit cancellation, which is the core of dimensional analysis. This approach is especially useful in scientific and engineering problems where unit consistency is critical.
