Zamiana ułamku okresowego
a) 2,(11)
b) 3,(2)
c) 4,1(7)
d) 2,(259)
x = 2,111....100x = 211,111...100x - x = 211,111... - 2,111..99x = 209/:99x = 209/99======================================b) 3,(2)x = 3,222....10x = 32,222...10x - x = 32,222... - 3,222...9x = 29/:9x = 29/9======================================
c) 4,1(7)x = 4,1777....100x = 417,777...100x - 10x = 417,777... - 41,777...90x = 376/:90x = 376/90======================================
d) 2,(259)x = 2,259...1000x = 2259,259....1000x - x = 2259,259... - 2,259...999x = 2257/:999x = 2257/999
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a)
2,(11)
x = 2,111....
100x = 211,111...
100x - x = 211,111... - 2,111..
99x = 209/:99
x = 209/99
======================================
b) 3,(2)
x = 3,222....
10x = 32,222...
10x - x = 32,222... - 3,222...
9x = 29/:9
x = 29/9
======================================
c) 4,1(7)
x = 4,1777....
100x = 417,777...
100x - 10x = 417,777... - 41,777...
90x = 376/:90
x = 376/90
======================================
d) 2,(259)
x = 2,259...
1000x = 2259,259....
1000x - x = 2259,259... - 2,259...
999x = 2257/:999
x = 2257/999