Question

Convert the following decimal to a fraction using Infinite Geometric Series.

Answer 1

Refer to the attachment.

Answer 2

Answer:

• let 5.477477477 be x

${ \rm{x = 5.477477477 \: - - - \{eqn(i) \}}}$

• Then let's find 1000x:

${ \rm{1000x = (1000 \times 5.477477477)}} \\ \\ { \rm{1000x = 5477.477477 - - - \{eqn(ii) \}}}$

• let's subtract eqn(i) from eqn(ii):

${ \rm{ \underline{ - \binom{1000x}{x} } = { \underline{ - \binom{5477.477477}{5.477477477} }}}} \\ { \rm{999x = 5472 \: \: \: \: \: \: \: \: \: \: \: \: }} \\ \\ { \rm{x = \frac{5472}{999} }}$

Answer: 5472/999