The fraction allows you to communicate length and tolerance in a single number. A decimal implies precision to the last number, a measure with a fraction can show 1/8 as more granular than 1/16. 1/8 of a cm is less precise than a mm, but if you wrote 1.125 cm, you are now implying sub mm level precision.
This matters because the level needed in building generally doesn’t line up to 1/10 measurements. For example if you had a brick wall and a row had 1 cm height differences between bricks in a row it would be extremely obvious and look terrible. A 1mm height difference would be impossible to notice, but is also overkill to get that level. Ideal is about 5/8 cm or 6.35 mm difference over 3 meters of wall. The fractional measure often ends up easier to work with in practice.




Exactly like my example above. 1/8 implies +or- 1/16. While .125 implies +or- .0005, but it was only measured to +or- .0625, which is 2 orders of magnitude different.