Not sure if decimal are allowed, but here's my attempt
1 operator, score 1.1765956249508713525610395676804...
$$123.4/56.789 \approx 2.17295603 \approx \pi - 0.96863662$$
3 operator, score 2.06714352383430453303221463889...
$$(1234/56)/(\lfloor7.89\rfloor) \approx 3.14795918 \approx \pi + 0.00636653 $$
$$(1234/56)/(\lfloor7.89\rfloor) \approx 3.14795918 \approx \pi + 0.00636653 $$