Question

transforme os decimais infitos periódicos em fração

a) 0,41111....
b)8,1333..
c)5,1777
d)2,31444​

Answer 1

Resposta:

a) 0,41111...

x=0,41111...

10x=4,1111...

9x=4

x=4/9

b)8,1333...

x=8,1333..

10x=81,333...

100x=813,333...

90x=732

x=732/90

c)5,1777...

x= 5,177...

10x= 51,777..

9x = 46

x = 46/9

d)2,31444..

x=2,31444..

100x=231,444...

99x= 229

x=229/99

Answer 2

Resposta:

$\times = \frac{4}{9}$

$\times = \frac{732}{90}$

$\times = \frac{46}{9}$

$\times = \frac{229}{99}$

Explicação passo-a-passo:

$0.41111... \\ \times = 0.41111... \\ 10 \times = 4.1111... \\ 9 \times = 4 \\ \times = \frac{4}{9}$

$8.1333... \\ \times = 8.13333... \\ 100 \times = 8.13333... \\ 90 \times = 732 \\ \times = \frac{732}{90}$

$5.1777... \\ \times = 5.1777... \\ 10 \times = 5.177... \\ 9 \times = 46 \\ \times = \frac{46}{9}$

$2.31444... \\ \times = 5.177... \\ 100 \times = 231.444... \\ 99 = 229 \\ \times = \frac{229}{99}$

Espero ter ajudado, abraços ☺