Let's analyze the student's process step-by-step to identify which conversion step was missing.
1. The student started with 1020 seconds.
2. He directly multiplied 1020 by [tex]\(\frac{1 \text{ hour}}{60 \text{ minutes}}\)[/tex], which he stated resulted in 17 hours.
This was incorrect because his step from seconds to hours skipped vital steps for proper conversion. The multiple-step conversion from seconds to hours involves intermediate conversion steps:
First, let's find out what was skipped by breaking down the conversion:
1. Convert seconds to minutes:
[tex]\[
1020 \text{ seconds} \times \left(\frac{1 \text{ minute}}{60 \text{ seconds}}\right)
\][/tex]
The correct conversion factor for seconds to minutes is [tex]\(\frac{1 \text{ minute}}{60 \text{ seconds}}\)[/tex]:
[tex]\[
1020 \text{ seconds} \times \left(\frac{1 \text{ minute}}{60 \text{ seconds}}\right) = 17 \text{ minutes}
\][/tex]
2. Convert minutes to hours:
Now that we have it in minutes, we need to convert minutes to hours:
[tex]\[
17 \text{ minutes} \times \left(\frac{1 \text{ hour}}{60 \text{ minutes}}\right)
\][/tex]
Given the correct conversion factor:
[tex]\[
17 \text{ minutes} \times \left(\frac{1 \text{ hour}}{60 \text{ minutes}}\right) \approx 0.2833 \text{ hours}
\][/tex]
Since [tex]\(\frac{1 \text{ minute}}{60 \text{ seconds}}\)[/tex] is the missing ratio that he did not use, let's identify the specifics of this step. The student skipped the essential ratio to transition from seconds to minutes, thereby only using one step to directly convert seconds to hours.
Thus, the conversion ratio he skipped is:
[tex]\[
\frac{1 \text{ minute}}{60 \text{ seconds}}
\][/tex]
Finally, the correct answer is option:
C. [tex]\(\frac{1 \text{ minute}}{60 \text{ seconds}}\)[/tex]
