數學問題(循環小數化分數)

數學問題(循環小數化分數)
1. 3.1 45 45 45 45......
=3.1+0.0454545…..
=31/10+45/990
=(31*99+45)/990
=3114/990
=173/55

2. 5.613 63 63 63......
=5.61+0.00363636….
=561/100+36/9900
=(561*99+36)/9900
=55575/9900
=247/44

3a. 0.3333......
=3/9
=1/3
3b. 由此，解方程(0.3333.....)x.=5/2
(1/3)x=5/2
x=(5/2)*3=15/2

1. x = 3.1 45 45 45 45......
100x = 314.5 45 45 45 45......
100x - x = 314.5 - 3.1
99x = 3114/10
x = 1038/330
考考你，為什麼要用100x 而不是10x 或1000x ?
用1000x 來做又有什麼分別?

2. x = 5.613 63 63 63......
100x = 561.363 63 63 63......
100x - x = 555.75
x = 55575/(100*99)
x = 337/12

3a x = 0.3333....
10x = 3.3333....
10x - x = 3
x = 1/3

3b 由此，解方程 x * 0.3333......=5/2
x* 1/3 =5/2
x =5/2 * 3
x =15/2

2011-09-08 19:15:13 補充：
=.= 我計錯數
第2題係 =247/44

第1顯冇約簡 173/55