Question

scrieti sub forma de fractie numerele : -0,72; 5,36; -0,(42); -3,(18); 0,5(3); 12,3(45); -7,6(543)

Answer 1

-0,72=-72/100=-18/25
5,36=536/100=134/25
-0,(42)=-42/99=-14/33
-3,(18)=-(318-3)/99=-315/99=-35/11
0,5(3)=(53-5)/90=48/90=8/15
12,3(45)=(12345-123)/990=12222/990=1358/110=679/55
-7,6(543)=-(76543-76)/9990=-76467/9990=-25489/3330

Answer 2

$\displaystyle -0,72=- \frac{72}{100} ^{(4} =- \frac{18}{25} \\ \\ 5,36= \frac{536}{100} ^{(4} = \frac{134}{25} \\ \\ -0,(42)=- \frac{42}{99} ^{(3} =- \frac{14}{33} \\ \\ -3,(18)=- \frac{318-3}{99} =- \frac{315}{99} ^{(9} =- \frac{35}{11} \\ \\ 0,5(3)= \frac{53-5}{90} = \frac{48}{90} ^{(6} = \frac{8}{15} \\ \\ 12,3(45)= \frac{12345-123}{990} = \frac{12222}{990} ^{(18} = \frac{679}{55}$

$\displaystyle -7,6(543)=- \frac{76543-76}{9990} =- \frac{76467}{9990} ^{(3} =- \frac{25489}{3330}$