I have a question that comes down to a 100 item sample with a mean of 0.5kg and a variance of 0.056kg. I am trying to calculate the 95% confidence interval. If I do the calculation using grams instead of Kg I get a different answer. I am assuming it's coming down to standard deviation being different as square root of 0.056 is larger while the square root of 56 is small.
Is there a rule or understanding I am missing around converting variance to standard deviation?