Question

forma fractiile zecimale periodice simple în fracții ordinare

Answer 1

A)
$0.(11) = \frac{11}{99}$
$2.(45) = 2 \frac{45}{99} = \frac{2 \times 99 + 45}{99} = \\ \frac{198 + 45}{99} = \frac{243}{99} \div 9= \frac{27}{11}$

$1.(23) = 1 \frac{23}{99} = \frac{1 \times 99 + 23}{99} = \frac{122}{99}$
$11.(243) = 11 \frac{243}{999} = \\ \frac{11 \times 999 + 243}{999} = \frac{10989 + 243}{999} =$
$= \frac{11232}{999} \div 9 = \frac{1248}{111}$
B)
$5.(6) = 5 \frac{6}{9} = \frac{5 \times 9 + 6}{9} = \frac{45 + 6}{9} = \frac{51}{9}$
$0.(30) = \frac{30}{99} \div 3 = \frac{10}{33}$
$12.(036) = 12 \frac{36}{999} = \\ \frac{12 \times 999 + 36}{999} = \frac{11988 + 36}{999} =$
$= \frac{12024}{999} \div 9 = \frac{1336}{111}$
$11.(423) = 11 \frac{423}{999} = \\ \frac{11 \times 999 + 423}{999} = \frac{10989 + 423}{999}$
$= \frac{11412}{999} \div 9 = \frac{1268}{111}$