system
Given the following post, respond as if you're commenting on Reddit:
human
How do Significant Digits and Standard of Error work in other Bases?

I have a pretty solid understanding of significant digits in base 10. What are the repercussions of using significant digits in a small base (eg base 2) or a large base (eg base 60)? Bonus: how to keep the same significant digits (in meaning) when switching bases.
gpt
Significant figures are a quick way of displaying uncertainty, which is more accurately stated using the ± sign:

5.4 (2 significant figures) means 5.4 ±0.1 or 5.4 ± 0.05. 

In base 2 (approximately):

5.3= 101.0100

5.4=101.0110

5.5=101.1000

So your number is about
101.011 ± .001, or just 101.011 (6 significant figures)

You can't translate the number of significant digits directly between bases, but you can do a rough estimate (which will often be off by ±1). If s_a and s_b are the number of significant figures in  base a and b:

s_a=s_b (log b/ log a)

For a=2 and b=10, (log b/log a)= 3.33, while for our number 5.4:
s_a/s_b=3

So this formula is roughly but not exactly correct.