注意到0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9=4.5
0.01+0.02+0.03+0.04+0.05+0.06+0.07+0.08+0.09=0.45
所以原式
=4.5+(0.1*9+0.45)+(0.2*9+0.45)+...+(0.9*9+0.45)
=4.5+(0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9)*9
+0.45*9
=4.5*10+0.45*10-0.45
=45+4.5-0.45
=49.05
注意到0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9=4.5
0.01+0.02+0.03+0.04+0.05+0.06+0.07+0.08+0.09=0.45
所以原式
=4.5+(0.1*9+0.45)+(0.2*9+0.45)+...+(0.9*9+0.45)
=4.5+(0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9)*9
+0.45*9
=4.5*10+0.45*10-0.45
=45+4.5-0.45
=49.05