解：?$(1)$?規(guī)定向北為正方向，
則向北行駛?$50\ \mathrm {km }$?記作?$+50\ \mathrm {km}，$?向南行駛?$40\ \mathrm {km}{記作}-40\ \mathrm {km}.$?
?$(2)$?購進大米?$200\ \mathrm {kg }$?記作?$+200\ \mathrm {kg}，$?賣出?$120\ \mathrm {kg}{記作}-120\ \mathrm {kg}.$?
?$(3)$?上升?$0.3\ \mathrm {m}{記作}+0.3\ \mathrm {m}，$?下降?$0.4\ \mathrm {m}{記作}-0.4\ \mathrm {m}，$?
下降?$0.2\ \mathrm {m}{記作}-0.2\ \mathrm {m}，$?上升?$0.8\ \mathrm {m}{記作}+0.8\ \mathrm {m}.$?
