Question

8) Encontre as frações geratrizes das dizimas periódicas a seguir:
a) 3,777...
b) 0.2555.
c) -12,181818...
d) 4,01313...​

Answer 1

A)

$x = 3.7 \\ 10x = 37.7 \\ \\ 10x = 37.7 \\ - x = 3.7 \\ \\ 9x = 34 \\ x = \frac{34}{9}$

B)

$x = 0.25 \\ 10x = 2.5 \\ 100x = 25.5 \\ \\ 100x = 25.5 \\ - 10x = 2.5 \\ \\ 90x = 23 \\ x = \frac{23}{90}$

C)

$x = - 12.18 \\ 100x = - 1218.18 \\ \\ 100x = - 1218.18 \\ - x = - 12.18 \\ \\ 99x = - 1206 \\ x = \frac{ - 1206}{99}$

D)

$x = 4.013 \\ 10x = 40.13 \\ 100x = 401.3 \\ 1000x = 4013.13 \\ \\ 1000x = 4013.13 \\ - 10x = 40.13 \\ \\ 990x = 3973 \\x = \frac{3973}{990}$