7/(n+8)
fractie zecimala finita
n+8 , descompus in factori primi trebuie sa contina numai puteri ale lui 2 sau 5
n+8=2^a *5^b
n+8=8=2³...... n=0
n+8=10 =2*5........ n=2
n+8=16=2^4......... n=8
n+8=20=2²*5.......... n=12
etc
fractie zecimala periodica simpla
b) n+8, descompus in factori trebuie sa contina numai puteri aleunor numere DIFERITEde 2 saude 5
n+8= x^a*y^b*.....*z^c
unde x, y, z∈N\{2;5}
n+8=3 n=-5 nu ni s-a cerut n natural am luat n intreg,n∈Z
n+8=7 n=-1
n+8=11 n=3
n+8=9=3².... n=1
n+8=13 n=5
n+8=17 n=11
n+8=19 n=11
n+8=21=3*7........ n=13
n+8=23 n=15
n+8=27=3³ n=19
n+8=29 n=21
n+8=31 n=23
n+8=33=3*11........ n=25
n+8=37............n=29
n+8=39=3*13.........n=31
etc
fractie zecimala periodica mixta
c) n+8= 2^a* 5^b* x^c *y^d....z^e
a si b nu sunt simultan nuli
c.d....e nu sunt simultan nuli
unde x,y, z∈N\{2;5}
adica descompunerea in factori primi a lui n+8 trebuie sa contina atat puteri ale lui 2 sau 5 cat si puteri ale unor numere diferite de 2 si diferite de 5
n+8=6 =2*3... n=-2
n+8=12=2²*3... n=4
n+8=15=3*5.... n=7
n+8=18=2*3²,,,,,,,, n=10
n+8=22=2*11....... n=14
n+8=24=2³*3... n=16
n+8=26=2*13........ n=18
n+8=28=2² *7....... n=20
n+8=30=2*3*5........ n=22
etc
