Does Converting Measurement Units Affect Error Values?

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Converting measurement units does not affect the actual error values; it only changes the representation of those values. In the discussion, the individual measured distances with a meter stick and estimated an error of 0.05 cm, which was converted to 0.0005 m. The TA argued that the error cannot be reduced simply by changing units, but the individual maintained that the percentage error remains consistent. The error propagation formula supports the idea that the error's magnitude is independent of the unit conversion. Ultimately, the conclusion is that the error value remains the same despite the change in units.
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I'm trying to do a lab writeup, and I'm going to include the uncertainty values as part of the data table. I was measuring distances with a meter stick with smallest divisions of 1mm, and estimated the error to be .05cm (.5mm - half the smallest division, as our TA told us was a good rule of thumb). However, having the data in (cm) was not useful, so I simply converted to (m), and the error along with it - the error of .05(cm) became an error of .0005(m). The TA, checking our data before we left the lab, told me that the conversion was wrong - that error can't get smaller just because you up-converted the data. I thought this was crazy because %error is still the same. She even pointed out the error propagation tables, showing me that the error for Z = a(B) ± C is dZ = a(dB), which seems to prove my point, not hers. Who is right?
 
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You are right. The error didn't change. Just the units.
 

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