Express the repeating decimal 0.513 (the 13 is repeating) as a fraction in lowest terms using the infinite geometric series method.

Answer 1

.513= .510+ 3/1000 + 3.10000+ 3/1E5 +3/1E6+ ...

notice that this is ...
= .510+ 3/1000 (1+ (1/10)+ (1/10)^3+..)
sum of
= .510 + 3/1000(1/.9)=+510/1000+3/900

= (510*9+300)/9000 check that
= (4590+ 300) /9000 = 4890/9000=489/900

Answer 2

the 1 and the there are repeating so it's .513131313131313... and 489/900 isn't giving me that. could you explain it again?

Answer 3

what 9,000=900x_