Question

Scrieti fractiile zecimale sub forma de fractii ordinare:
4,2(3);5,12(8)9,6(71);11,56(23);109,3(405);0,29(978);2,88(0985);56,12(3)

Answer 1

$4.2(3) = 4 \frac{23 - 2}{90} = 4 \frac{21}{90} = 4 \frac{7}{30} = \frac{4 \times 30 + 7}{30} = \frac{127}{30}$

$5.12(8) = 5 \frac{128 - 12}{900} = 5 \frac{116}{900} = 5 \frac{58}{450} = \frac{5 \times 450 + 58}{450} = \frac{2250 + 58}{450} = \frac{2308}{450}$

$9.6(71) = 9 \frac{671 - 6}{990} = 9 \frac{665}{990} = 9 \frac{133}{198} = \frac{9 \times 198+ 133}{198} = \frac{1782+ 133}{198} = \frac{1915}{198}$

$11.56(23) = 11 \frac{5623 - 56}{9900} = 11 \frac{5567}{9900} = \frac{11 \times 9900 + 5567}{9900} = \frac{108900 + 5567}{9900} = \frac{114467}{9900}$

$109.3(405) = 109 \frac{3405 - 3}{9990} = 109 \frac{3402}{9990} = 109 \frac{1701}{4995} = 109 \frac{567}{1665} = \frac{109 \times 1665 + 567}{1665} = \frac{181485 + 567}{1665} = \frac{182052}{1665} = \frac{60684}{555} = \frac{20228}{185}$

$0.29(978) = \frac{29978 - 29}{99900} = \frac{29949}{99900} = \frac{9983}{33300}$

$2.88(0985) = 2 \frac{880985 - 88}{999900} = 2 \frac{880897}{999900} = \frac{2 \times 999900 + 880897}{999900} = \frac{1999800 + 880897}{999900} = \frac{2880697}{999900}$

$56.12(3) = 56 \frac{123 - 12}{900} = 56 \frac{111}{900} = 56 \frac{37}{300} = \frac{56 \times 300 + 37}{300} = \frac{16800 + 37}{300} = \frac{16837}{300}$