How do you convert -1.3 (3 repeating) to a fraction?

##-4/3 =-1 1/3##

Let's call ##x = -1. color(red)(3333333)...## then ##10 x = -13. color(red)(3333333)....##

Subtract ##10x-x## to get:

##9x = -12. color(red)(0000)...larr ##all the decimals will subtract to give 0.

##9x = -12##

##x = -12/9= -4/3##

##-4/3 =-1 1/3##

Note that in this case only 1 digit recurred, so we multiplied by 10.

If 2 digits recur, multiply by 100. If 3 digits recur, multiply by 1000 and so on.

The denominators of the fractions obtained in this way will always be 9, 99, 999 and so on.