Question

va rog ajutor aici algebra​

Answer 1

Răspuns:

$1) \: 0.(3) = \frac{3}{9} = \frac{1}{3} \\ 0.1(6) = \frac{16 - 1}{90} = \frac{15}{90} = \frac{1}{6} \\ 0.91(6) = \frac{916 - 91}{900} = \frac{825}{900} = \frac{165}{180} = \frac{33}{36} = \frac{11}{12}$

$2)0.(6) = \frac{6}{9} = \frac{2}{3} \\ 0.3(6) = \frac{36 - 3}{90} = \frac{33}{90} = \frac{11}{30} \\ 1.2(3) = \frac{123 - 12}{90} = \frac{111}{90} = \frac{37}{30}$

$3)0.(15) = \frac{15}{99} = \frac{5}{33} \\ 4.2(3) = \frac{423 - 42}{90} = \frac{381}{90} = \frac{127}{30} \\ 0.45(3) = \frac{453 - 45}{900} = \frac{408}{900} = \frac{102}{225} = \frac{34}{75}$

$4) \: 0.(45) = \frac{45}{99} = \frac{6}{11} \\ 0.5(3) = \frac{53 - 5}{90} = \frac{48}{90} = \frac{8}{15} \\ 0.3(45) = \frac{345 - 3}{990} = \frac{342}{990} = \frac{38}{110} = \frac{19}{55}$

$5)0.(108) = \frac{108}{999} = \frac{12}{111} = \frac{4}{37} \\ 0.0(5) = \frac{5}{90} = \frac{1}{18} \\ 1.58(3) = \frac{1583 - 158}{900} = \frac{1425}{900} = \frac{285}{180} = \frac{57}{36} = \frac{19}{12}$

$6)2.(18) = \frac{218 - 2}{99} = \frac{216}{99} = \frac{24}{11} \\ 0.01(6) = \frac{16 - 1}{900} = \frac{15}{900} = \frac{3}{180} = \frac{1}{60} \\ 0.0(72) = \frac{72}{990} = \frac{8}{110} = \frac{4}{55}$

$7)0.2(7) = \frac{27 - 2}{90} = \frac{25}{90} = \frac{5}{18} \\ 2.1(6) = \frac{216 - 21}{90} = \frac{195}{90} = \frac{39}{18} = \frac{13}{6} \\ 0.5(6) = \frac{56 - 5}{90} = \frac{51}{90} = \frac{17}{30}$

$8)0.6 = \frac{6}{10} = \frac{3}{5} \\ 6.75 = \frac{675}{100} = \frac{135}{20} = \frac{27}{4} \\ 0.025 = \frac{25}{1000} = \frac{5}{200} = \frac{1}{40}$

$9)2.32 = \frac{232}{100} = \frac{116}{50} = \frac{58}{25} \\ 17.5 = \frac{175}{10} = \frac{35}{2} \\ 34.75 = \frac{3475}{100} = \frac{695}{20} = \frac{139}{4}$