  We give a~detailed construction of the complete ordered field of real numbers
by means of infinite decimal expansions. We prove that in the canonical
encoding of decimals neither addition nor multiplication is {\em computable},
but that both operations are {\em weakly computable}; we introduce both kinds
of computability in greater generality. We determine which additive and
multiplicative shifts (restrictions of addition and multiplication to one
variable) are computable, and prove that each of these shifts becomes
computable after a~permutation of encoding. We ask if it is the case for the
bivariate addition and multiplication.
