Hello,
That's false!
Let's take an example
m=0.123456789 kg =123.456789 g=123456.789 mg
a=123.46 g ==> 4 digits exact.
b=123456.79 mg ==>7 digits exact
|m-a|=|-0,003211|=0,003211
|m-b|=|-0,001|=0,001
As 0.001<0.003211 ==>|m-b|<|m-a| the error is less for b.