To determine which of the following is a valid conversion factor, we need to examine each one carefully:
1. [tex]\(\frac{1 \, \text{cm}^3}{1 \, \text{L}}\)[/tex]:
- We know that [tex]\(1 \, \text{L} = 1000 \, \text{cm}^3\)[/tex].
- Thus, [tex]\(1 \, \text{cm}^3\)[/tex] is not equal to [tex]\(1 \, \text{L}\)[/tex].
- [tex]\(\frac{1 \, \text{cm}^3}{1 \, \text{L}}\)[/tex] is not a valid conversion factor.
2. [tex]\(\frac{1 \, \text{mL}}{100 \, \text{L}}\)[/tex]:
- We know that [tex]\(1 \, \text{L} = 1000 \, \text{mL}\)[/tex].
- Thus, [tex]\(100 \, \text{L} = 100 \times 1000 \, \text{mL} = 100000 \, \text{mL}\)[/tex].
- Therefore, [tex]\(\frac{1 \, \text{mL}}{100 \, \text{L}}\)[/tex] is not correct because 1 mL is much smaller than 100 L.
3. [tex]\(\frac{10 \, \text{m}}{1 \, \text{dm}}\)[/tex]:
- We know that [tex]\(1 \, \text{m} = 10 \, \text{dm}\)[/tex].
- Therefore, [tex]\(10 \, \text{m} = 10 \times 10 \, \text{dm} = 100 \, \text{dm}\)[/tex].
- [tex]\(\frac{10 \, \text{m}}{1 \, \text{dm}}\)[/tex] is not a valid conversion factor.
4. [tex]\(\frac{100 \, \text{cm}}{1 \, \text{m}}\)[/tex]:
- We know that [tex]\(1 \, \text{m} = 100 \, \text{cm}\)[/tex].
- Therefore, [tex]\(\frac{100 \, \text{cm}}{1 \, \text{m}}\)[/tex] is a correct and valid conversion factor.
Given this, the valid conversion factor is:
[tex]\[
\frac{100 \, \text{cm}}{1 \, \text{m}}
\][/tex]
Thus, the answer is [tex]\(\frac{100 \, \text{cm}}{1 \, \text{m}}\)[/tex].
