Question

Here is a widely publicized, true story about how failing to convert units resulted in a huge loss. in 1998, the mars climate orbiter probe, instead of entering orbit, crashed into the surface of mars. the resulting inquiry revealed that nasa navigators had been making minor course corrections in si units, whereas the software written by the probe's makers implicitly used british units. in the united states, most scientists use si units, whereas most engineers use the british (or imperial) system of units. (interestingly, british units are not used in the united kingdom.) for these two groups to be able to communicate with each other, unit conversions are necessary. the unit of force in the si system is the newton, n, which is defined in terms of basic si units as 1n=1(kg⋅m)/s2. the unit of force in the british system is the pound, lb, which is defined as 1lb=1(slug⋅ft)/s2, where the slug is the unit of mass.

Answer 1

This is the reason why dimensional analysis is very important. It is a technique used that only involves operations with units. You disregard the quantities first. The concept is to make sure that the final answer of your calculations must be consistent of what is asked. Similar units are cancelled when they appear both on the numerator and denominator side. If the mathematicians used this, they could've prevented the crash from happening. What good would the calculations bring if you are not consistent with the units?