循環小數化分數點計???

(1) Let x = 0.(6)

10 x = 6.(6)

Then 10 x - x = 6

9x = 6

x = 2 / 3

(2) Let x = 0.7(44)

10x = 7.(44)

100x = 74.(44)

Then 100x - 10x = 67

90x = 67

x = 67 / 90

( 3 ) Let x = 0.(45 )

100x = 45.(45)

Then 100x - x = 45

99x = 45

x = 5 / 11

( 4 ) Let x = 0.9(4)

10 x = 9.(4)

100x = 94. (4)

Then 100x - 10x = 85

90x = 85

x = 17 / 18

( 5 ) Let x = 0.(148)

1000x = 148.( 148)

Then 1000x - x = 148

999x = 148

x = 4 / 27

( 6 ) Let x = 0.5(678)

10x = 5.(678)

10000x = 5678.(678)

Then 10000x - 10x = 5673

9990x = 5673

x = 1891/3330

1. 0.66666666666666666.............=x
10x=6.66666666666666666666666666666666................
9x=6.000000000000000............................
x=2/3

2. 0.7444444444444444444444444..............=x
100x=74.44444444444.........................
90x=67.00000000000000000000000
x=67/90

3. 0.4545454545454545.................=x
100x=45.45454545.................
99x=45.00000000................
x= 45/99

4. 0.9444444444444444............=x
100x=94.4444444444444444444444.............
90x=85.0000000000000000000000..........
x= 85/90
= 17/18

5. 0.148148148..................=x
1000x=148.148148148.....................
999x=148.0000000000000000000000000.........
x=148/999
=4/27

6. 0.5678678678678678...........=x
10000x=5678.678678678............
9990x=5673.0000000000000000....................
x=5673/9990
=1891/3330