  The Dirichlet forms methods, in order to represent errors and their
propagation, are particularly powerful in infinite dimensional problems such as
models involving stochastic analysis encountered in finance or physics, cf.
[5]. Now, coming back to the finite dimensional case, these methods give a new
light on the very classical concept of 'numerical approximation' and suggest
changes in the habits. We show that for some kinds of approximations only an
Ito-like second order differential calculus is relevant to describe and
propagate numerical errors through a mathematical model. We call these
situations strongly stochastic. The main point of this work is an argument
based on the arbitrary functions principle of Poincar\'e-Hopf showing that the
errors due to measurements with graduated instruments are strongly stochastic.
Eventually we discuss the consequences of this phenomenon on the specification
of an approximate numerical result.
