Question

dizimas fracionais 1,444

Answer 1

A dizima fracionária de 1,444 é $\frac{13}{9}$
porque 13 dividido pra 9 é igual a 1,444...

Answer 2

$\sf{1,444=1+\underbrace{0,44... +0,0044...+...}_{soma~dos~termos~da~P.G~infinita}}\\\sf{a_1=0,44=\dfrac{44}{100}}\\\sf{a_2=0,0044=\dfrac{44}{10000}}\\\sf{q=\dfrac{a_2}{a_1}}\\\sf{q=\dfrac{\frac{44}{10000}}{\frac{44}{100}}}$

$\sf{q=\dfrac{\diagdown\!\!\!\!44}{100\diagup\!\!\!0\diagup\!\!\!0}\cdot\dfrac{1\diagup\!\!\!0\diagup\!\!\!0}{\diagdown\!\!\!\!44}=\dfrac{1}{100}}\\\sf{S_n=\dfrac{\frac{44}{100}}{1-\frac{1}{100}}}\\\sf{S_n=\dfrac{\frac{44}{100}}{\frac{99}{100}}}\\\sf{S_n=\dfrac{44}{\diagup\!\!\!1\diagdown\!\!\!\!\!\!00}\cdot\dfrac{\diagup\!\!\!1\diagdown\!\!\!\!\!\!00}{99}}\\\sf{S_n=\dfrac{44\div11}{99\div11}}$

$\huge\boxed{\boxed{\boxed{\boxed{\sf{S_n=\dfrac{4}{9}}}}}}$

$\sf{1,444...=1+\dfrac{4}{9}=\dfrac{13}{9}}$