3.83 repeating as a fraction?

1 Answer
Jun 25, 2018

It depends upon how much of the given number you mean to be repeating.

Explanation:

#3.8bar3color(white)("xxxxx")#only the last digit #3# repeats:

#10x=color(white)("x")38.33333...#
#ul(-x)color(white)(=)ul(-color(white)(3)3.83333...#
#99x = color(white)("x")34.5#
#rarr x=(34.5)/90=23/60#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#3.bar(83)color(white)("xxxxxx")# the last 2 digits are repeating:

#100x=color(white)("x..")383.838383...#
#ul(-color(white)("..")x)=ul(-color(white)("xx")3.838383...)#
#color(white)(".")99x=color(white)("xx")380.0#
#rarr x=380/99#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#bar(3.83)color(white)("xxxxxx")#all 3 digits repeat:

#1000x =color(white)("..")3833.83383383...#
#ul(-color(white)("xx")x)=ul(-color(white)("....")3.83383383383...)#
#color(white)(".")999x=color(white)(".")3830.0#
#rarr x= 3830/999#