循環小數化分數

Q1. x = 0.6666...
10x = 6.666...
10x - x = 6.666.... - 0.6666... = 6
9x = 6, x = 6/9 = 2/3.
Q2. 0.7444.... = 0.7 + 0.0444... = 0.7 + 0.4444/10.
Let x = 0.444...
10x = 4.4444...
10x - x = 9x = 4, x = 4/9
so 0.74444 = 0.7 + 4/90 = 7/10 + 4/90 = (63 + 4)/90 = 67/90.
Q3.
x = 0.454545...
100x = 45.4545...
100x - x = 99x = 45, so x = 45/99= 5/11.
Q4.
0.9444... = 0.9 + 0.4444/10 = 9/10 + 4/90 = (81 + 4)/90 = 85/90 = 17/18
Q5. You mean 0.14888888.... or 0.148148148.....?
Q6. You mean 0.5678888... or 0.567856785678... ?



2009-08-24 14:47:27 補充：
Q5. 0.148148148... = 148/999. 0.14888888... = 67/450. Q6. 0.56785678... = 5678/9999.
0.5678888888.... = 5111/9000.

只要唔要重覆之後果d數字就是了