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The relative error puts the size of the error into context.
An absolute error of 10, in a number whose value is 1 indicates a range of -9 to 11 for the true value. This means that telling you that the value is 1 is near enough pointless. On the other hand, an absolute error of 10 in a number whose value is 1 billion means that the true value is somewhere in the range 999,999,990 and 1,000,000,010. I suggest that the discrepancy is not significant.
The relative error in the first case is 1000% and in the second, it is 1 millionth of 1%.
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