Запишите в виде рационального числа периодическую дробь:
а) −0,(3);
б) −1,(2);
в) −2,(5);
г) −0,(17);
д) −3,(18);
е) −1,(05);
ж) 2,(0);
з) −0,(0);
и) 4,37(0).
−0,(3)
x = −0,(3)
10x = −3,(3)
10x − x = −3,(3) − (−0,(3))
9x = −3,(3) + 0,(3)
9x = −3
−1,(2)
x = −1,(2)
10x = −12,(2)
10x − x = −12,(2) − (−1,(2))
9x = −12,(2) + 1,(2)
9x = −11
−2,(5)
x = −2,(5)
10x = −25,(5)
10x − x = −25,(5) − (−2,(5))
9x = −25,(5) + 2,(5)
9x = −23
−0,(17)
x = −0,(17)
100x = −17,(17)
100x − x = −17,(17) − (−0,(17))
99x = −17,(17) + 0,(17)
99x = −17
−3,(18)
x = −3,(18)
100x = −318,(18)
100x − x = −318,(18) − (−3,(18))
99x = −318,(18) + 3,(18)
99x = −315
−1,(05)
x = −1,(05)
100x = −105,(05)
100x − x = −105,(05) − (−1,(05))
99x = −105,(05) + 1,(05)
99x = −104
2,(0) = 2
−0,(0) = 0
4,37(0) = 4,37
