The relationship between the kilogram and the pound is defined exactly as:

1 lb = 0.453 592 37 kg

Note that the pound is defined as a proportion of the kilogram and not the other way around, so it is not strictly correct to say that 1 kg = 1/0.453 592 37 lb - even ignoring the fact that this reciprocal is not exact when expressed to eight significant figures as in the definition.