My TA has me confused about how to use scientific notation when margin of error and orders of magnitude are involved.
The number I wrote: 3.78 ± 0.02 * 10^-3
My TA told me that this means: 3.78 ± 0.00002
I thought that this meant: 0.00378 ± 0.00002
Which one is correct? I've been looking online to find something that explains the proper notation when writing out margin of error with orders of magnitude but I haven't been able to find anything (I'm at a loss of what terms to search for). If what I wrote isn't the correct way to say 0.00378 ± 0.00002, then what is? Writing it as 3.78 * 10^-3 ± 0.02 or 3.78 * 10^-3 ± 0.02 * 10^-3 seems kind of foolish.
