Question

Determine a geratriz:
a) 0,324545...
b) 6,5252...
c)3,52333...
d)0,414141...
e)2,12323...
f)2,421...

Answer 1

$a) ~0,324545...\to~~ \dfrac{3245-32}{9900} \to~~ \dfrac{3213}{9900} \to~~ \large\boxed{~\dfrac{357}{1100}~}\\\\\\\\ b)~ 6,5252...\to~~ 6+ \dfrac{52}{99} \to~~ \dfrac{594+52}{99} \to~~ \large\boxed{~\dfrac{646}{99}~}\\\\\\\\ c)~3,52333... \to~~3+ \dfrac{523-52}{900} \to~~ 3+ \dfrac{471}{900} \to~~ \dfrac{2700+471}{900} \to~~ \\\\ \dfrac{3171}{900} \to~~\large\boxed{~\dfrac{1057}{300}~}$



$d)~0,414141...\to~~ \large\boxed{~\dfrac{41}{99}~} \\\\\\\\ e)~2,12323...\to~~ 2+ \dfrac{123-1}{990} \to~~ 2+\dfrac{122}{990} \to~~ \dfrac{1980+122}{990} \to\\\\ \dfrac{2102}{990} \to~~ \large\boxed{~\dfrac{1051}{495}~}\\\\\\\\ f)~2,421... \to~~ 2+ \dfrac{421}{999}\to~~ \dfrac{1998+421}{999}\to~~ \large\boxed{~\dfrac{2419}{999}~}$