解:设x=0.=0.5555…
那么10x=5.=5+0.(利用倍数关系构造了另一个有同样循环节的数)
所以10x﹣x=5.﹣0.=5,解得x=
所以,0.=.这样我们就将无限循环小数0.化为了分数.
(1)试着用上述方法将无限循环小数0.,0.分别化为分数.
(2)将无限循环小数2.化为分数.
同类型试题
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2
y = sin x, x∈R, y∈[–1,1],周期为2π,函数图像以 x = (π/2) + kπ 为对称轴
y = arcsin x, x∈[–1,1], y∈[–π/2,π/2]
sin x = 0 ←→ arcsin x = 0
sin x = 1/2 ←→ arcsin x = π/6
sin x = √2/2 ←→ arcsin x = π/4
sin x = 1 ←→ arcsin x = π/2