Question

Calcule as seguintes geratrizes 

a) 1,040404...
b) 11,444...
c) 2,027027...
e) 0,501501...
f) 1,3232...
g) 4,333...
h) 1,2424...
i) 1,888....
j) 5,018018....
k)8,333....

Answer 1

a) 1,040404 = 104-1/99 = 102/99

b) 11,444 = 114-11/9=103/9

c)2,027027 = 2027-2/999 = 2025/999

e) 0,501501 = 0501-0/999 = 501/999

f) 1,3232 = 132-1/99= 131/99

g)4,333 = 43 - 4/9 = 39/9

h)1,2424 = 124-1/99=123/99

i)1,888 = 18-1/9 = 17/9

j)5,018018= 5018-5/999 = 5013/999

k)8,333 = 83-8/9= 75/9

Answer 2

a) x= 1,040404...
100x = 104,040404...
100x-x=104,0404...-1,0404...
99x=103
x= $\frac{103}{99}$

b) x=11,444...
10x=114,444...
10x-x=114,444...-11,444...
9x=103
x=$\frac{103}{9}$

c) x=2,027027...
1000x=2027,027027...
1000x-x=2027,027027...
999x=2025
x=$\frac{2025}{999}$

e)x= 0,501501...
1000x=501,501501...
1000x-x=501,501501...-0,501501...
999x=501
x=$\frac{501}{999}$

f) x=1,3232...
100x=132,3232...
100x-x=132,3232...-1,3232...
99x=131
x=$\frac{131}{99}$

g) x=4,333...
10x=43,333...
10x-x=43,333...-4,333...
9x=39
x=$\frac{39}{9}$

h) x=1,2424...
100x=124,2424...
100x-x=124,2424...-1,2424...
99x=123
x=$\frac{123}{99}$

i)x= 1,888....
10x=18,888...
10x-x=18,888...-1,888...
9x=17
x=$\frac{17}{9}$

j)x= 5,018018....
1000x=5018,018018...
1000x-x=5018,018018...
999x=5013
x=$\frac{5013}{999}$

k)x=8,333....
10x=83,333...
10x-x=83,333...-8,333...
9x=75
x=$\frac{75}{9}$