Question

transformar as dizimas periódicas em fração : 
a) 0,333
b)1,444
c) 2,1555

Answer 1

$a)\;10x=3,333...\\ ~~~~~~~x=0,333...$

$\Longrightarrow9x=3$

$x=\dfrac{3}{9}=\dfrac{1}{3}$

$0,333...=\dfrac{1}{3}$

$b)\;10x=14,444...\\ ~~~~~~~x=1,444..$

$\Longrightarrow9x=13$

$x=\dfrac{13}{9}$

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

$c)\;100x=215,555...\\ ~~~~~~~10x=21,555...$

$\Longrightarrow90x=194$

$x=\dfrac{194}{90}=\dfrac{97}{45}$

$2,1555...=\dfrac{97}{45}$