Question

Escreva a fração geratriz de:
0,787878
0,134444
2,88888
0,5666666

Answer 1

Resposta:

$0,787878... = \\ \\ x = 0,787878... \times( 10) \\ 10x = 7,87878... \times (10) \\ 100x = 78,787878... \\ \\ 100x - x = 78,787878... - 0,787878... \\ \\ 99x = 78 \\ \\ { x = \dfrac{78 \div 3}{99 \div 3} } \\ \\ \green{ x = \dfrac{26}{33} }$

$0,134444... \\ \\ x = 0,134444 ... \times (10) \\ 10x = 1,34444... \times (10) \\ 100x = 13,4444... \times (10) \\ 1000x = 134,444... \\ \\ 1000x - 100x = 134,444... - 13,4444... \\ \\ 900x = 121 \\ \\ \green{ x = \dfrac{121}{900} }$

$2.8888.... \\ x = 2,8888... \times (10) \\ 10x = 28,888... \\ \\ 10x - x = 28,888... - 2,888... \\ \\ 9x = 26 \\ \\ \green{ x = \dfrac{26}{9} }$

$0,56666... = \\x = 0,56666... \times (10) \\ 10x = 5,666... \times (10) \\ 100x = 56,666... \\ \\ 100x - 10x = 56,666... - 5,6666... \\ \\ 90x = 51 \\ \\ \green{x = \dfrac{51}{90} }$

Bons Estudos!