In the scientific world the units we use are important. In engineering they can be the difference between something working or not. NASA famously lost its $125 million Mars Climate Orbiter due to a maths error with units. An Air Canada employee forgot to convert between metric and imperial units, which caused them to under-fill by 50% and run out of fuel mid-f light (nobody was killed). Christopher Columbus used Roman miles rather than nautical miles to measure distance — he landed in the Bahamas thinking it was Asia.
Understanding the relationships between base and derived units can be very helpful, leading to a greater understanding of why things behave the way they do (either in a practical task or in a calculation). I regularly stress the importance of knowing and understanding the units with which we work. As part of this, I insist that students learn the units that accompany the formulae.
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