I am a digital artist designer and illustrator and I, also, worked for many years as an aerospace draughtsman and later doing the same at the very beginning of Computer Aided Draughting and Design ( CADD ) for a few aerospace companies in my surrounding location.
I work with fractions and decimals and converting fractions to decimals and decimals to fraction a WHOLE lot in my lines of work!
There are, also, formulas for converting DPI/ppi to different units
And different units converted to DPI/ppi.
I use these formulas on a regular and daily basis.
I did the DPI/ppi to U.S. inch calculation first.
Then I did the U.S. standard inch conversion to metric centimeters ( cm ) conversions, next.
I have used many different types of formulas in my work for very many years.
Also, some drawing/painting programs on both computers and mobile devices can do the conversion faster and automatically based on inputted digital drawing document sizes ( pixels or other units of measure ) and/or DPI/ppi.
The calculations are correct and accurate, and slightly rounded up for simplicity.
You have all the information that you need, now.
Good Luck to You!