`平方根&循環小數轉分數的問題-{10分}

求下列各數的平方根:
1,169
169 = 13x13
所以平方根是 13

2,729
729 = 27x27
所以平方根是 27

3,1024
1024 = 32x32
所以平方根是 32

把下列各循環小數化為分數:( )<---加上=上方有點
1, 0.(6)
用代數解
x = 0.(6) ___(1)
10x = 6.(6) ___(2)
兩式相減
9x = 6
x = 6/9
x = 2/3

2, 0.7(4)
x = 0.7(4)
10x = 7.(4) ___ (3)
100x = 74.(4) ___(4)
(4) 式減 (3)式
90x = 67
x = 67/90

3, 0.(4)(5)
x = 0.(4)(5) ___ (5)
100x = 45.(4)(5) ___ (6)
(6) 減 (5)
99x = 45
x = 45 / 99
x = 5/11

4, 0.9(4)
x = 0.9(4)
10x = 9.(4) ___ (7)
100x = 94.(4) ___ (8)
(8) 減 (7)
90x = 85
x = 85/90
x = 17/18

5, 0.(1)4(8)
x = 0.(1)4(8) ___ (9)
1000x = 148.(1)4(8) ___ (10)
(10) 減 (9)
999x = 148
x = 148/999

6, 0.5(6)7(8)
x = 0.5(6)7(8)
10x = 5.(6)7(8) ___ (11)
10000x = 5678.(6)7(8) ___ (12)
(12) 減 (11)
9990x = 5673
x = 5673/9990
x = 1891/3330

平方根:13, 27, 32
循環小數化為分數:2/3(知一個)

169=13*13
729=9*81=3^6=27*27
1024=64*16=32*32

0.66666.........=0.3333333333333............*2=2/3
0.7444444.......=0.7+0.044444444444........=7/10+ =.=
0.94444......=9/10+ =.=
對5起,5識

1) 13
2) 27
3) 32




1) 33/50
2) 1861/2500
3) 909/2000
4) 118/125
5) 37/250
6) 2839/5000