Question

encontre a fração geratriz de 2,3939... e mostre que ela é diferente de 2,4.

Answer 1

$\bullet\;\; x=2,3939\ldots\\ \\ 100x=239,3939\ldots\\ \\ \\ 100x-x=239,\mathbf{3939\ldots}-2,\mathbf{3939\ldots}\\ \\ 99x=237+2,\mathbf{3939\ldots}-2,\mathbf{3939\ldots}\\ \\ 99x=237\\ \\ x=\dfrac{237}{99}\\ \\ x=\dfrac{237 \div 3}{99 \div 3}\\ \\ x=\dfrac{79}{33}\\ \\ 2,3939\ldots=\dfrac{79}{33}$


$\bullet\;\; 2,4=\dfrac{24}{10}\\ \\ 2,4=\dfrac{12}{5}$


É evidente que

$2,3939\ldots \neq 2,4$

pois

$\dfrac{79}{33} \neq \dfrac{12}{5}\\ \\ 79 \cdot 5 \neq 33 \cdot 12\\ \\ 395 \neq 396$

Answer 2

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}2,3939... = \\\\2+0,3939... = \\\\2+\frac{39}{99} = \\\\2+\frac{13}{33} =\\\\\frac{66+13}{33} = \\\\ \frac{79}{33} \end{array}\right$

PROVA DA DIFERENÇA:

$\boxed{ 2,4 = \frac{24}{10} = \frac{12}{5}}$

$\boxed{\boxed{\frac{79}{33} \neq \frac{12}{5} \to 12*33 \neq 79*5 \to 396 \neq 395 }}$

Espero ter ajudado. =^.^=