Question

Transformați în fracții ordinare ireductibile :
a)0,1(3); e)12,1(7); i)0,1(253);
b)0,2(7); f)5,12(3); j)0,12(71);
c)1,1(3); g)5,0(5); k)0,2(152);
d)2,5(4); h)1,13(27); l)1,7(317).

Answer 1

Transformam fractiile periodice mixte in fractii ordinare astfel:
la numarator avem numarul ca si cand n-ar avea nici virgula, nici perioada, minus partea neperiodica, iar la numitor atati de 9 cate cifre are perioada, si atati de 0 cate zecimale neperiodice avem.

a) 0,1(3)=(13-1)/90=12/90=4/30=2/15
b)0,2(7)=(27-2)/90=25/90=5/18
c)1,1(3)=(113-11)/90=102/90=51/45=17/15
d)2,5(4)=(254-25)/90=229/90
e. 12,1(7)=(1217-121)/90=1196/90=598/45
f. 5,12(3)=(5123-512)/900=4611/900=1537/300
g. 5,0(5)=(505-5)/90=500/90=50/9
h. 1,13(27)=(11327-113)/9900=11214/9900=1246/1100=623/550
i. 0,1(253)=(1253-1)/9990=1252/9990=626/4995
j. 0,12(71)=(1271-12)/9900=1259/9900
k. 0,2(152)=(2152-2)/9990=2150/9990=215/999
l. 1,7(317)=(17317-17)/9990=17300/9990=1730/999