What is the correct/standard way to check if difference is smaller than machine precision?

I often end up in situations where it is necessary to check if the obtained difference is above machine precision. Seems like for this purpose R has a handy variable: .Machine$double.eps. However when I turn to R source code for guidelines about using this value I see multiple different patterns.

Examples

Here are a few examples from stats library:

t.test.R

if(stderr < 10 *.Machine$double.eps * abs(mx))

chisq.test.R

if(abs(sum(p)-1) > sqrt(.Machine$double.eps))

integrate.R

rel.tol < max(50*.Machine$double.eps, 0.5e-28)

lm.influence.R

e[abs(e) < 100 * .Machine$double.eps * median(abs(e))] <- 0

princomp.R

if (any(ev[neg] < - 9 * .Machine$double.eps * ev[1L]))

etc.

Questions

1. How can one understand the reasoning behind all those different 10 *, 100 *, 50 * and sqrt() modifiers?
2. Are there guidelines about using .Machine$double.eps for adjusting differences due to precision issues?