Actually, as @Henry mentions in comments
[...] the logarithm of the ratio [...] might make some sort of sense.
And given that you are using US CPI as base, you are very likely to want the logarithm of the ratio. Why ?
What would you do If I were asking you to compute the growth rate (relative difference) of two aggregates, say, productions (e.g. of cars), denoted by $Q$, between two consecutive years $t$ and $t+1$ ? Actually, you would use the following formulae:
$g_{t}^{d} = \frac{Q_{t+1}-Q_{t}}{Q_{t}} = -1 + \frac{Q_{t+1}}{Q_{t}}$
where $^{d}$ stands for discrete. Indeed, note that when one computes $g_{t}^{d}$ like so, there is an implicit assumption. This assumption is that we reasonably suppose our productions to be discrete values. If we were considering those as continuous values (e.g. liters of water), we would actually use an other formulae, as follows
$g_{t}^{c} = \ln{\left(\frac{Q_{t+1}}{Q_{t}}\right)}$
Note that $g_{t} \rightarrow g_{t}^{c}$ when $Q_{t+1}\rightarrow Q_{t}$.
Thus, we just compared two types of production over time, conditioning the formulae that is used to what these productions are (discrete versus continuous).
What if I were asking you to compare CPIs over two nations ?