Question

transforma fractiile zecimale periodice simple in fractii ordinare a)0,(11);1,(23);2(45);11,(243);b)5,(6);0,(30);12,(036);11,(423).

Answer 1

$a)0.(11) = \frac{11}{99}$

$1.(23) = \frac{123 - 1}{99} = \frac{122}{99}$

$2.(45) = \frac{245 - 2}{99} = \frac{243}{99} = \frac{81}{33} = \frac{27}{11}$

$11.(243) = \frac{11243 - 11}{999} = \frac{11232}{999} = \frac{3744}{333} = \frac{1248}{111} = \frac{416}{37}$

$b)5.(6) = \frac{56 - 5}{9} = \frac{51}{9} = \frac{17}{3}$

$0.(30) = \frac{30}{99} = \frac{10}{33}$

$12.(036) = \frac{12036 - 12}{999} = \frac{12024}{999} = \frac{4008}{333} = \frac{1336}{111}$

$11.(423) = \frac{11423 - 11}{999} = \frac{11412}{999} = \frac{3804}{333} = \frac{1268}{111}$