What is the value of $0.01\log_{10}$?
Differences in log scales correspond to ratios of the underlying values.  Saying you are within .01 on a $\log_{10}$ scale means the true value is within $10^{-.01}$ and $10^{.01}$ of the stated value, ratio wise.  That calculates out to 0.9772 and 1.0233.  Since the value is so close to 1, an interval on the ratio scale is close to an interval on a difference scale, so you could also say the results are within about 2.3%.

I haven't read the paper.

Hope this helps.

Ced



Followup:

So, on a whim I looked up "centibel" and found https://en.wiktionary.org/wiki/centibel.  A "cB" if you will.  Not too many other references though.

I should have also looked at the OP's math link.  The correct answer was already there.