No I am not sure about your math but I don’t think it is right… I rarely deal with the metric- imperial divide, except with products.
So I think you mean you are starting with a model and you know the metric
sizes. (or even a real object) at full scale, and you want to know how big it is in (or scale it down to ) 1/8" = 1’-0" scale.
SketchUp can do it for you of course as Dave says OR in SU you can also scale the model by the correct ratio, and then just change the units.
To do so you should know the ratio that relates to the scale. In this case it is 1:96. So you just scale the model down 1/96. Oddly SU won’t take this number. but you can use the decimal .01.
If you have a real object at 118 cm. it would measure. 1.18 cm in a 1/8"=1’-0" scale drawing, (which is roughly .5 inches).
To get the ratio you divide by 12 so 1/8 / 12=.01 or 1:96. Also e.g. 3"=1’-0" is .25 or 1:4 scale ratio.
The equation 118/8=14.75 = 14’-7" is suspect. I’d leave that process out altogether. Maybe this is the new math and it’s too late at night here, but I’d do it differently.
You seem to be wanting to make both a scale drawing and units conversion. However, you don’t want to mix the two. Deal with these separately. I wonder what the assignment or purpose is.
Your conversion to the table’s dimension look close. but for scaling the drawing, all that’s needed is the ratio, and that tells you what the drawing will scale down to.
Also I think you are using the decimal incorrectly. The decimal number in the imperial system does not relate to “feet and inches”, It can only relate to one or the other . For an example civil engineering plans often use decimal feet. However 10.5’ is NOT 10’-5", it is 10’-6", because there are 12 inches in a foot.
If you are a metric user, you can now get an idea what we suffer with in the U.S. But we have to keep on top of this for the near future or we may mess up our space missions terribly.
In SketchUp we usually draw at 1:1 and only make it a scale drawing in the printing or LayOut process.
In a final gasp of pedantry: If you are doing furniture drawings. 1/8"=1’-0" is probably too small a scale to be useful.