Question

4. Transformați următoarele numere zecimale în fracții ordinare ireductibile:
a) 0,7; 5,6; 0,118; 4,12; 3,25; 12,19; 0,085; 1,05; 24,64; 0,0005;
b) 0,(3); 0,(61); 5,(12); 1,(123); 0,(234); 3,(81); 0,(2403); 16,(72);
c) 0,1(3); 0,12(3); 3,2(15); 2,5(7); 10,04(5); 5,3(27); 1,31(5); 0,236(4​

Answer 1

Răspuns:

Explicație pas cu pas:

a) 0,7=7/10;  5,6=56/10=28/5;  0,118=118/1000=59/500;  4,12=412/100=403/25; 3,25=325/100=13/4;  12,19=1219/100; 0,085/1000=17/500;  1,05=105/100=51/50; 24,64=2464/100=616/25;   0,0005=5/10 000=1/5000;

b) 0,(3)=1/3; 0,(61)=61/99;   5,(12)=512/100=128/25;  

1,(123)=1123/999;    0,(234)=234/999=26/111;    3,(81)=381/99=127/33;

0,(2403)=2403/9999=267/1111);    16,(72); =1672/99

c) 0,1(3)=(13-1)/90=12/90=2/15;

0,12(3)=(123-12)/900=111/900=37/3000;

3,2(15)=(3215-32)/990=3183/990=1061/330

2,5(7)=(257-25)/90=232/90=116/45

10,04(5)=(10045-1004)/900=9041/900

5,3(27)=(5327-53)/990=5274/990=586/110=293/55

1,31(5)=(1315-131)/900=1184/900=296/225

0,236(4​)=(2364-236)/9000=2128/9000=532/2250=266/1125