EE Armando Gaban ( Matemática – nonos anos A, B e C)
Encontre as frações geratrizes das dízimas que seguem:
a-) 3,88888 ...
b-) 5,77777 ...
c-) 1,333333 ...
d-) 7,111111 ...
e-) 3,444444 ...
f-) 7,666666 ...
g-) 4,131313 ...
h-) 10,36363636 ...
i-) 0,79797979 ...
j-) 7,38383838 ...
k-) 5,81818181 ...
l-) 3,90909090 ...
m-) 6,0909090909 ...
Respostas
Resposta:
1a) 3,888.....
3,888.... = x . (10)
38,888.... = 10x
10x - x =38 - 3
9x = 38 - 3
9x = 35
x = 35/9
b) 5,777...
5,777.... = x . (10)
57,777... = 10x
10x - x = 57 - 5
9x = 52
x = 52/9
c) 1,333.....
1,333..... = x . (10)
13,333.... = 10x
10x - x = 13 - 1
9x = 12
x = 12/9
x = 4/3
d) 7,111....
7,111.... = x . (10)
71,111.... = 10x
10x - x = 71 - 7
9x = 64
x = 64/9
e) 3,444....
3,444.... = x . (10)
34,444.... = 10x
10x - x = 34 - 3
9x = 31
x = 31/9
f) 7,666....
7,666.... = x . (10)
76,666.... = 10x
10x - x = 76 - 7
9x = 69
x = 23/3
g) 4,131313.....
4,131313.... = x . (100)
413,131313.... = 100x
100x - x = 413 - 4
99x = 409/99
x = 409/99
h) 10,363636.....
10,363636.... = x . (100)
1036,363636.... = 100x
100x - x = 1036 - 10
99x = 1026
x = 114/11
i) 0,797979.....
0,797979... = x . (100)
79, 797979... = 100x
100x - x = 79 - 0
99x = 79
x = 79/99
j) 7, 383838...
7,383838... = x . (100)
738,383838... = 100x
100x - x = 738 - 7
99x = 731
x = 731/99
k) 5,818181...
5,818181.... = x . (100)
581,818181.... = 100x
100x - x = 581 -5
99x = 576
x = 576/99
l) 3,909090...
3,909090... = x . (100)
390,909090..... = 100x
100x - x = 390 - 3
99x = 387
x = 387/99
m) 6,090909....
6,090909 = x . (100)
609,090909...
100x - x = 609 - 6
99x = 603
x = 603/99