Question

Bài 1 : Viết dưới dạng phân số tối giản :
a, 0,(24)
b, 0,2(45)
c, 2,5(324)
d, 0,5(3)
Bài 2:
Rút gọn M = 0,5 + 0,(3) - 0,1(6)/ 2,5 + 1,(6) - 0,8(3)

Answer 1

Bài 1:
a) 0,24 = 6/25
b) 0,245 = 49/200
c) 2,5324 = 5/2
d) 0,5 = 1/2

Answer 2

a) \(0,\left(24\right)=\frac{24}{99}=\frac{8}{33}\)

b)\(0,2\left(45\right)=\frac{245-2}{990}=\frac{243}{990}=\frac{27}{110}\)

c)\(2,5\left(324\right)=2+0,5\left(324\right)=2+\frac{5324-5}{9990}=2+\frac{197}{370}=\frac{937}{370}\)

d) \(0,5\left(3\right)=\frac{53-5}{90}=\frac{48}{90}=\frac{8}{15}\)

Bài 2 : \(M=\frac{0,5+0,\left(3\right)-0,1\left(6\right)}{2,5+1,\left(6\right)-0,8\left(3\right)}\)

\(M=\frac{\frac{1}{2}+\frac{1}{3}-\frac{16-1}{90}}{\frac{5}{2}+\frac{5}{3}-\frac{83-8}{90}}\)

\(M=\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{6}}{\frac{5}{2}+\frac{5}{3}-\frac{5}{6}}=\frac{\frac{1}{2}+\frac{1}{3}-\frac{1}{6}}{5\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{6}\right)}=\frac{1}{5}\)