First I have to make an assumption: that when you say "they are into business" you do not mean "professionals" in general -because if they are, say, engineers building bridges or spacecrafts, they should and most probably do care a lot about whatever mathematical toll can give them increased precision. So my assumption is that "into business" means "into business administration" (I won't bother discussing the "politics" part).
Then, from my experience as a "business person", I suggest (for precision's shake) that you separate "business people" (let's call them BP's), into those that are in the Financial Services Sector, and those that are not.
The first group has as a usual level of precision four decimal digits, the "basis points": interest rates are usually quoted as percentages with two decimal digits: $6.23$% $= 0.0623$. Of course, in very large contracts this can go further, but I am stating the usual everyday practice.
The second group, well, they haven't decided yet: business reports, charts, "contribution margins" etc are quite often expressed also as above... but almost nobody will talk, communicate, think, negotiate or decide at that level of precision. 2 decimal digits (i.e. whole percentages and nothing more, $6% = 0.06$), is the usual level here...
...for percentages. because when you go into levels of magnitudes, then you loose at least 3 zeros before the dot: The amount $100.450$ USD is "a hundred thousand", while if the business is in the tens of millions, well, we talk using tens of millions (only accountants resist this, and this is why BP's call them derogatorily "bean counters").
But this apparent avoidance of precision, perhaps surprisingly, means that BP's should adore things like $\sqrt 2$. Why?
Well, why are they not after precision in the first place? Because, there is always the trade-off between the gains from precision and the cost of attaining it.This cost is measured in time units: time required to think precisely, time required to compute precisely...
...and BP's are obsessed (rightfully) with efficient time management. So they will take anything that cuts the time to do anything: $\sqrt 2$ requires less button pushes compared to its rational approximation -and so it increases precision at a time gain: that's a dream come true (I am not joking). BP's will still think of $\sqrt 2$ as "about $1.5$" -but when it comes to actual computing, $1.5$ takes three button hits, while $\sqrt 2$ takes only two.
So it appears that if you want to push this agenda, your chance is to make the BP's see the reality that, with all these computers and calculators around, they can think in whatever level of precision they like -but that it is in their time-management interest to compute using these strange looking mathematical concepts and tools...while avoiding also the possibility of fatal compounding approximation error: a dream come true.