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標題:
將循環小數化為分數
發問:
將循環小數化為分數 0.*6 0.7*4(4有循環小數點) 0.*4*5(4and5有循環小數點) 0.9*4(4有循環小數點) 0.*14*8 0.5*67*8
最佳解答:
1. 0.6666 = x 10x = 6.6666 10x - x = 6.6666 - 0.666 = 6 9x = 6 x = 6/9 = 2/3. 2. 0.744444 = x 0.74444 - 0.7 = x - 0.7 0.044444 = x - 0.7...................(1) 0.44444= 10x - 7.....................(2) (2) - (1) we get 10x - 7 - (x - 0.7) = 0.444444 - 0.0444444 = 0.4 10x - 7 - x + 0.7 = 0.4 9x = 7 + 0.4 - 0.7 = 6.7 x = 67/90. 3. 0.454545 = x 100x = 45.454545 100x - x = 45.454545 - 0.454545 = 45 x = 45/99= 5/11. 4. 0.9444444 = x 0.94444 - 09 = x - 0.9 0.044444 = x - 0.9..............(1) 10x - 9 = 0.444444..............(2) (2) - (1) we get 10x - 9 -(x - 0.9) = 0.444444 - 0.044444 = 0.4 10x - 9 -x + 0.9 = 0.4 9x = 9 + 0.4 - 0.9 = 8.5 x = 85/90 = 17/18. 5. 0.148148148 = x 1000x = 148.148148 1000x - x = 148.148148 - 0.148148 = 148 999x = 148 x = 148/999. 6. 0.56785678 = x 10000x = 5678.56785678 10000x - x = 5678.56785678 - 0.56785678 = 5678 9999x = 5678 x = 5678/9999.
其他解答:6CC7293C789E3310
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