Question

DEtermine a fraçao geriatriz das dizimas 3,4444. 10,050505. 503333. 1,6777

Answer 1

3,44444... = 3+0,4444...

0,4444=x
4,444=10x subtraindo as equações temos que

4=9x x=4/9, então 3+4/9 = (27+4)/9 = 31/9

10,0505050= 100,505050/10 = (100+0,505050)/10

0,505050=x
50,505050=100x subtraindo as equações

50=99x ===> x=50/99

(100+50/99)/10 = (9900+50)/99/10  = 9950/990 = 995/99

5,0333= 50,333/10 = (50+0,333)/10

0,333=x
3,3=10x  => x=3/9 ou 1/3

(50+1/3)/10 = (150+1)/3/10 = 151/30

1,67777 = 16,777/10 = (16+0,777)/10

0,777=x
7,777=10x   => x=7/9

(16+7/9)/10 = (144+7)/9/10 = 151/90