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.