Question #a1e8f

2 Answers
Jan 6, 2017

Answer:

#0.6bar(12) = 101/165#

Explanation:

Let #x = 0.6bar(12)#

Note that the repeating portion of the decimal is #2# digits long, so we multiply #x# by #10^2 = 100#.

#100x = 61.2bar(12)#

#=> 100x-x = 61.2bar(12)-0.6bar(12)#

#=> 99x = 61.2-0.6#

#=> 99x = 60.6#

#=> 99x = 606/10#

#=> x = 606/10 * 1/99#

#:. x = 101/165#

For a detailed approach to general questions of this type, see this question.

Jan 6, 2017

Answer:

#101/165#

Explanation:

Note that #0.6bar(12)# is the same as #0.612121212...#

Let #x=0.6bar(12)#

Then #10x=6.121212...#

and #1000x=612.121212...#

So #1000x-10x= 612.121212...#
#" "ul(color(white)(61)6.121212...) larr" subtract"#
#" "1000x-10x=606.000000.....#

#=>x(1000-10)=990x=606#

#=>x=606/990 = 101/165#