If you were asked to convert 25 cg to the unit hg, which of the following would be the first fraction used in the conversion?
1 hg/10^2
10^2/1hg
10^2 hg/ 1cg
10^-2 g/1 cg
I would convert to g first.
To convert from centigrams (cg) to hectograms (hg), we need to establish a conversion factor between these two units. A conversion factor is a fraction that represents the relationship between the two units.
In this case, the conversion factor is going to have the unit hg in the numerator (top) and the unit cg in the denominator (bottom). This is because we want to cancel out cg and end up with hg.
Let's analyze the given options:
1. 1 hg/10^2: This option is not suitable because it does not have the unit cg in the denominator, which is necessary for cancelling out cg.
2. 10^2/1 hg: This option is also not correct because it has cg in the numerator and hg in the denominator, which is the reverse of what we want.
3. 10^2 hg/1 cg: This option is the correct choice. It has hg in the numerator and cg in the denominator, allowing us to cancel out cg and convert to hg.
4. 10^-2 g/1 cg: This option is unrelated to the conversion from cg to hg. It involves converting between grams (g) and centigrams (cg), which is not what we need.
So, the correct choice would be 10^2 hg/1 cg, as it represents the appropriate conversion factor for converting 25 cg to hg.