Let's evaluate each of the given operations to find out which one makes the number 317.5 equal to 3.175.
### Option A: Multiply 317.5 by [tex]\(10^2\)[/tex]
[tex]\[ 317.5 \times 10^2 = 317.5 \times 100 = 31750 \][/tex]
This result is not equal to 3.175.
### Option B: Divide 317.5 by [tex]\(10^3\)[/tex]
[tex]\[ 317.5 \div 10^3 = 317.5 \div 1000 = 0.3175 \][/tex]
This result is not equal to 3.175.
### Option C: Divide 317.5 by [tex]\(10^2\)[/tex]
[tex]\[ 317.5 \div 10^2 = 317.5 \div 100 = 3.175 \][/tex]
This result matches our target value, 3.175.
### Option D: Multiply 317.5 by [tex]\(10^3\)[/tex]
[tex]\[ 317.5 \times 10^3 = 317.5 \times 1000 = 317500 \][/tex]
This result is not equal to 3.175.
### Conclusion
Among the given operations, only dividing 317.5 by [tex]\(10^2\)[/tex] (Option C) results in 3.175.
Therefore, the correct answer is:
C. Divide 317.5 by 10².
