Significant figures tells us that about how may digits we can count on to be precise given the uncertainty in our calculations or data measurements.
Since, one inch = 2.54 cm.
This is equivalent as saying that 1.0000000.. inch = 2.540000... cm.
Since the inch to cm conversion doesn't add any uncertainty, so we are free to keep any and all the significant figures.
Since, being an exact number, it has an unlimited number of significant figures and thus when we convert inch to cm we multiply two exact quantities together. Therefore, it will have infinite number of significant figures.
