Question

3. Determine a fração geratriz das dizimas periódicas simples a seguir. Sempre que possível sie
plifique as frações

a) 0,0045 em dízima=
b) 5444…=

Answer 1

$\large\boxed{\begin{array}{l}\rm a)~\sf x=0,04545\dotsc\cdot1000\\\sf 1000x=45,4545\cdot100\\\sf 100000x=4545,4545\dotsc\\-\underline{\begin{cases}\sf 100000x=4545,454545\dotsc\\\sf1000x=45,454545\dotsc\end{cases}}\\\\\sf99\,000x=4500\\\sf x=\dfrac{4500\div4500}{99000\div4500}\\\\\sf x=\dfrac{1}{22}\end{array}}$

$\Large\boxed{\begin{array}{l}\rm b)\\\sf x=0,5444\dotsc\cdot10\\\sf 10x=5,444\dotsc\cdot10\\\sf 100x=54,444\dotsc\\-\underline{\begin{cases}\sf 100x=54,444\dotsc\\\sf 10x=5,444\dotsc\end{cases}}\\\sf 90x=49\\\\\sf x=\dfrac{49}{90}\end{array}}$