一道简便计算.0.12+0.23+0.34+0.45+0.56+0.67+0.78注意最后一位是循环的,如,0.12222…+0.23333…

Question

一道简便计算.
0.12+0.23+0.34+0.45+0.56+0.67+0.78
注意最后一位是循环的,如,0.12222…+0.23333…

Answer 1

正如
1/9 = 0.111……是 1 循环
1/3 = 0.333……是 3 循环,1/3 = 3/9
1/99 = 0.010101……是 01 循环
1/11 = 0.090909……是 09 循环,1/11 = 9/99
题目
0.1222 + 0.2333 + 0.3444 + 0.4555 + 0.5666 + 0.6777 + 0.7888
= ( 1.222 + 2.333 + 3.444 + 4.555 + 5.666 + 6.777 + 7.888 ) / 10
= ( 1+ 2+ 3+ 4+ 5+ 6+ 7+ 2/9 + 3/9 + 4/9 + 5/9 + 6/9 + 7/9 + 8/9 ) / 10
= ( 28 + 35/9 ) / 10
= 28/10 + 35/90
= 30/10 - 2/10 + 35/90
= 3 - 18/90 + 35/90
= 3+ 17/90
或者
= ( 28 + 27/9 + 8/9 ) / 10
= ( 28 + 3 + 0.888 ) / 10
= 2.8 + 0.3 + 0.0888
= 3.1888……是 8 循环