How do you convert -5.7 (7 repeating) as a fraction?

1 Answer
Mar 24, 2016

#a=5 7/9#

Explanation:

Let the required number be #a =- 5.dot7# .....(1)
Multiply both sides with #10#, as there is one repeating digit therefore multiply with #10^1#
#10a = -57.dot 7# .....(2)

Subtracting (1) from (2)

#10a - a = -57.dot 7 - (-5. dot7)#
#=>9a = -57.dot 7 +5. dot7#

or #9a = -52#

Solving for the required fraction
#a = 52/9=5 7/9#