Question

determine a fração geratriz das seguintes dizimas periódicas a)1,4242 b)0,382382 c)0,34545... d)1,23888...

Answer 1

a) 1,4242...

x = 1 + 0,4242...
x = 1 + 42/99
x = 141/99

b) 0,382382...
x = 382/999

c) 0,34545...
10x = 3,4545...
10x = 3 + 0,4545...
10x = 3 + 45/99
10x = 342/99
990x = 342
x = 342/990

d) 1,23888...
100x = 123,888..
100x = 123 + 8/9
100x = 1115/9
900x = 1115
x = 1115/900

Answer 2

a)
$1.4242..... = 1 \times \frac{42}{99} = \frac{141}{99}$
simplificando ficará 47/33.

b)
$0.382382.... = \frac{382}{999}$
c)
$0.34545.... = \frac{345 - 3}{990} = \frac{342}{990}$
simplificando ficará 171/495.

d)
$1.23888.... = 1 \times \frac{238 - 23}{900} = 1 \times \frac{215}{900} = \frac{1115}{900}$
simplificando ficará 223/180.