Przedstaw liczby 0,333... i 0,3636... w postaci ułamka zwykłego.
Dam naj. Z góry dzięki ;))
0,3333...... = 0,(3)
0,(3) = x / * 10
3,(3) = 10x / - x
3,(3) - 0,(3) = 10x - x
3 = 9x
x = 3/9
x = 1/3
0,(3) = 1/3
0,3636...... = x / * 100
36,36... = 100x / - x
36,36... - 0,36... = 100x - x
36 = 99x
x = 36/99
x = 4/11
0,3636.... = 4/11
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0,3333...... = 0,(3)
0,(3) = x / * 10
3,(3) = 10x / - x
3,(3) - 0,(3) = 10x - x
3 = 9x
x = 3/9
x = 1/3
0,(3) = 1/3
0,3636...... = x / * 100
36,36... = 100x / - x
36,36... - 0,36... = 100x - x
36 = 99x
x = 36/99
x = 4/11
0,3636.... = 4/11