What is -0.5(3 repeating) written as a fraction?

1 Answer
Alan P.
Nov 14, 2015

#-5.333bar3 = -16/3#

Explanation:

Lets for simplicity initially ignore the minus sign.

Let #x=5.33333...#
therefore
#color(white)("XXX")10x=53.33333...#
from which is follows that
#color(white)("XXX")9x = 53.3333... - 5.3333... =48#
and (dividing by #9#)
#color(white)("XXX")x=48/9 = 16/3#

If #5.3333... = x = 16/3#
then
#-5.3333... = -16/3#

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