Răspuns :

Miky93id
0,(1)=1/9

0,(12)= 12/99= 4/33

0,(123)= 123/999= 42/333

1/9 +12/99 +123/999=  aducem la acelasi numitor  (890109)

(98901 + 12 *8991 + 123 *891)/890109=

=(98901+107892+  109593)/890109=

= 316386/890109=

=35154/98901=

=11718/32967=

=3906/10989=

=434/1221

b)1,2(3)= 1 intreg (23-2)/90=  1 intreg 21/90= 1 intreg 7/30= 37/30

2,02(03)=2 intregi (203-2)/9900= 2 intregi 201/9900= 2 intregi 67/3300=

= 6667/3300

3,1(012)=3 intregi (1012-1)/9990= 3 intregi 1011/9990=

=30981/9990  =10327/3330

37/30 + 6667/3300 +10327/3330=  aducem la acelasi numitor  (10989000)

(37*366300 + 6667 *3330 + 10327 * 3300)/ 10989000=

= (13553100 + 22201110 + 34079100)/10989000=

= 69833310/10989000=

= 6983331/1098900=

=2327777/366300
SKAWPid
a)0,(1)+0,(12)+0,(123)= 1/9 +12/99 +123/999=(98901 + 12 *8991 + 123 *891)/890109=(98901+107892+  109593)/890109=316386/890109=434/1221


b)1,2(3)+2,02(03)-3,1(012)= 37/30 + 6667/3300 +10327/3330(37*366300 + 6667 *3330 + 10327 * 3300)/ 10989000= (13553100 + 22201110 + 34079100)/10989000=69833310/10989000= 2327777/366300

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