Question

Convert the recurring decimal 6.838383 into an fraction???

Answer 1

\[ \frac{677}{99} \]

Answer 2

Exercise for you, convert \[ 6.7845838383838383\cdots \] to rational.

Answer 3

\[\text{ let } x=6.838383838...\]
\[\text{ then } 100x=683.838838383...\]

Answer 4

http://www.wolframalpha.com/input/?i=6.7845838383838383...
DAMN I'm good.

Answer 5

now do 100x-x

Answer 6

\[99x=683-6\]

Answer 7

solve for x

Answer 8

\[99x=677 => x=\frac{677}{99}\]

Answer 9

myin, do you know the one liner trick? ;)

Answer 10

@strawberry how do you feel about that?

Answer 11

pretty confident now

Answer 12

i multiply x by 100 because i seen that the 83 was repeating