某人将3.57777.....乘一数时，误把3.57777.....写成3.57，结果与正确答案相差1.4，那么正确答案是多少

设被乖数为X.

设 0.0777...=a 则:100a = 7.7777... 10a = 0.7777...
得:90a =100a-10a = 7.7777...- 0.7777... = 7
得:a = 7/90
3.5777...= 3.5 + a = 3.5 + 7/90
依题意有: (3.5 + 7/90) *X - (3.5+0.07) *X = 1.4
得:X* 7/90 - X*7/100 = 1.4
解得:X = 180

正确答案是(3.5 + 7/90)*180 = 644

设 0.0777...=a 则:100a = 7.7777... 10a = 0.7777...
得:90a =100a-10a = 7.7777...- 0.7777... = 7
得:a = 7/90
3.5777...= 3.5 + a = 3.5 + 7/90
依题意有: (3.5 + 7/90) *X - (3.5+0.07) *X = 1.4
得:X* 7/90 - X*7/100 = 1.4
解得:X = 180

正确答案是(3.5 + 7/90)*180 = 644

设这个数是X
3.57777X=3.57X+1.4
解得=180.18
所以正确答案是3.57777*180.18=644.6

644

简单演算
0.0077777777........=7/900
7/900*t=1.4
t=180
180*3.57=642.6
642.6+1.4=644

你去问华罗庚吧

我的答案也是644.6