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

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Answer 1 · 2016-08-29T22:14:20

#-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.