Everywhere I look, I see the following as the list of formulas for converting metric to SI:
C * 1.8 + 32 = F
Km / 1.609344 = Mi
mm / 25.4 = in
m/s * 2.236936 = mph
However, the first and the 3rd do not seem very precise. Are there more precise formulas available? If so what are they?
Places I have looked: Google, MathOverflow (not sure if this question belongs there, as no related questions I could find there matched this, but some exist here), wikipedia.
All of these proposed the same set of formulas, but all of them also described the C->F conversion as the "Easy" conversion formula.
According to Wikipedia Fahrenheit, the Fahrenheit scale places the freezing point of water at 32 and the boiling point at 212. This is 180 degrees apart. In Celsius it is 0 and 100 respectively 100 degrees apart. 180/100 = 1.8 which is why the conversion factor is exactly 1.8. As such the temperature conversion is accurate based on the arbitrary points chosen for the freezing and boiling of water.
As for the 1 inch = 25.4 mm, this was set as the standard inch in 1930 by the British Standards Institution, and adopted by the American Standards Association in nearly all matters in 1933. The exception was in Survey Data when measuring deeds. This means that the standard inch is 25.4 mm and the survey inch is 1/39.37 meters. Wikipedia Inch
This leads me to the conclusion that the reason why the conversions for temperature and length use numbers that appear imprecise is simply by engineering when they designed the systems. As such there is no need for extra digits of precision in these two cases.