First, 10 links is not 119,5 mm. The pins on the chain are half an inch apart. Counting 10 pins would give you 5 inches, or 12,7 cm (1 inch = 25,4 mm).
Where are your measurement reference points? Usually one would measure from the center of one pin to the center of the next reference link. You can use the edges of the links if you find that easier, but I don't find the accuracy of my method to be a problem. When a chain is (sufficiently) worn, you will be able to see it even if you eyeball the reference points.
See the image below (excuse the dirty background). The five links of the brand new lower (thicker, single-speed) chain are almost exactly 5 inches long (lens distortion, camera angle etc. may skew the measurement, but I assure you the chains are aligned and the caliper shows 5" exactly):
Note that the green and brown lines capture 5 inches of the chain, the blue line on top only captures 4 links. Sorry if this is confusing.
NB: The problem I've had is that measuring just a handful of links gives iffy results. Maybe if the chain is tensioned and on the bike, this works well, but laying them flat on a table, I can never get a nice result. I couldn't tell from my own image, nor from the 5 inches of chain right in front of me, that the top (narrower, 10-speed) chain pictured, is used, and warrants replacement. Thankfully, while the relative error stays constant, the absolute error increases with the length of the chain. Pictured below is this same 10-speed chain over a brand new chain, but after 10 inches (I did my best to keep them aligned at the reference link, ten inches to the left):
I personally don't trust cheap chain measuring tools to be able to measure this with any sort of repeatability. What chances are there for a stamped piece of metal to be accurate to within 1% at 127 mm? I compare the chain with a brand new one, across the 114 links supplied, which will show you immediately and without a doubt whether your old chain is stretched. I also don't see the value in spending $20 or more on a more expensive tool given that a new chain will cost me less.