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

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

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

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

1. a) -0,35 = -7/20 ; b) 1,14 = 57/50

  c) 2,108 = 527/250 ; -0,725 = -29/40

2. a) 0,2(3) = 0,2 + 0,0(3) = 0,2 + 0,3. 0,(1) = 0,2 + 0,3.1/9 = 1/5 + 1/30 = 7/30 

  b 1,4(51) = 1,4 + 0,0(51) = 7/5 + 5,1. 0,(01) = 7/5 + 5,1. 1/99 = 7/5 + 17/330 = 479/330

  c) -2,(412) = -2 - 0,(412) = -2 - 412. 0,(001) = -2 - 412. 1/999 = -2 - 412/999 = -2410/999

d) 3,1(45) = 3,1 + 0,0(45) = 3,1 + 4,5. 0,(01) = 3,1 + 4,5 . 1/99 = 3,1 + 1/22 = 173/55

3. Ta có: -2,(6).x = 0,1(6)

=> [-2 - 0,(1).6].x = (0,1 + 0,6. 0,(1)]

=> (-2 - 2/3)x = 0,1 + 1/15

=> -8/3x = 1/6

=>  x = 1/6 : (-8/3)

=> x = -1/16

\(=\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+...+\dfrac{1}{19}-\dfrac{1}{20}\)

\(=\dfrac{1}{4}-\dfrac{1}{20}=\dfrac{5-1}{20}=\dfrac{4}{20}=\dfrac{1}{5}\)

\(0,1\left(2\right)=\frac{12-1}{90}=\frac{11}{90}\)

\(0,\left(27\right)=\frac{27}{99}=\frac{3}{11}\)

\(3,\left(42\right)=3+\frac{42}{99}=\frac{113}{33}\)

\(3,\left(45\right)=3+\frac{45}{99}=\frac{38}{11}\)

=38/11 nhé

bạn nha

Hok tốt

\(0,1\left(2\right)\)\(=\frac{12-1}{90}\)\(=\frac{11}{90}\)

\(0,\left(27\right)\)\(=\frac{27}{99}\)\(=\frac{3}{11}\)

\(3,\left(42\right)\)\(=3+\frac{42}{99}\)\(=\frac{113}{33}\)

\(3,\left(45\right)\)\(=3+\frac{45}{99}\)\(=\frac{38}{11}\)

a)

b)

0,(6)=2/3

0,(24)=8/33

2,(1485)=217/101

0,6=2/3

0,24= 6/25

2,1485=217/101

0,1(2)=\(\frac{12-1}{90}=\frac{11}{90}\)

0,0(8)=\(\frac{8-0}{90}=\frac{4}{45}\)

3,2(45)=\(3+\frac{245-2}{990}=3+\frac{27}{110}=\frac{357}{110}\)

-0,34(567)=\(-\frac{34567-34}{99900}=-\frac{1279}{3700}\)

3,(1)=3+0,(1)=3+\(\frac{1}{9}\)=\(\frac{28}{9}\)