Question

As frações geratrizes referentes às dízimas periódicas 0,45555... e 2,555... são

Answer 1

$\boxed{\begin{array}{l}\sf x=0,4555\dotsc\cdot10\\\sf 10x=4,555\dotsc\cdot10\\\sf 100x=45,555\dotsc\\\sf 100x=41+4,555\dotsc\\\sf100x=41+10x\\\sf 100x-10x=41\\\sf90x=41\\\sf x=\dfrac{41}{90}\end{array}}$

$\boxed{\begin{array}{l}\sf x=2,555\dotsc\cdot10\\\sf10x=25,555\dotsc\\\sf 10x=23+2,555\dotsc\\\sf 10x=23+x\\\sf 10x-x=23\\\sf 9x=23\\\sf x=\dfrac{23}{9}\end{array}}$