Question

Determine a fração geraria de
A)7,1888...
B)4,12
C)3,12
D)0,0444...

Answer 1

a)

$m=7,1888... \times100\\100m=718,888\times10(1)$

$1000m=7188,888...(2)$

$(2)-(1):\:-\begin{cases} 1000m=7188,888... \\100m=718,888... \end{cases}$

$900m=6470\\m=\dfrac{647\cancel0}{90\cancel0}\\\bf{m=\dfrac{647}{90}}$

b)

$y=4,1222... \times100\\100y=412,222\times10(1)$

$1000y=4122,222...(2)$

$(2)-(1):\:-\begin{cases} 1000y=4122,222... \\100y=412,222...\end{cases}$

$900y=3710\\y=\dfrac{371\cancel0}{90\cancel0}$

$\bf{y=\dfrac{371}{90}}$

c)

$g=3,1222... \times100\\100g=312,222\times10(1)$

$1000g=3122,222...(2)$

$(2)-(1):\:-\begin{cases} 1000g=3122,222... \\100g=312,222...\end{cases}$

$900g=2810\\g=\dfrac{281\cancel0}{90\cancel0}$

$\bf{g=\dfrac{281}{90}}$

d)

$w=0,0444... \times100\\100w=4,444...\times10(1)$

$1000w=44,444... (2)$

$(2)-(1):\:-\begin{cases} 1000w=44,444... \\100w=4,444...\end{cases}$

$900w=40\\w=\dfrac{4\cancel0}{90\cancel0}$

$w=\dfrac{4\div2}{90\div2}$

$\bf{w=\dfrac{2}{45}}$