熟練掌握循環(huán)小數和分數的轉化就簡單了.這里把推導全寫出來.
一、
0.027027……
= 27×0.001001……
= 27×（0.001001……×111）/111
= 27×0.1111……/111
= 27×1/9×1/111
= 3/111
= 1/37
0.179672179262……
= 179672×0.000001000001……
= 179672×（0.000001000001……×111111）/111111
= 179672×1/9×1/111111
= 179672/999999
0.027027……×0.179672179672……
= 1/37 × 179672/999999
= 4856/999999
= 4856 × 1/999999
= 4856 ×1/9 ×1/111111
= 4856 ×（0.111111 111111 …… /111111）
= 4856 × 0.000001 000001 ……
= 0.004856 004856 004856 ……
100÷ 6 = 16 …… 余4,因此一百位小數的最后4位就是0048 （56……）,
四舍五入,最后1位就是9.
二、
2.1818……
= 2 + 18×0.0101……
= 2 + 18×（0.0101……×11）/11
= 2 + 18×0.1111……/11
= 2 + 18×1/9×1/11
= 2 + 2/11
= 24/11
24/11×（A + 1） = 218/100
解得A = -1/1200