How do you convert repeating decimals into fractions?

1 Answer
Mar 30, 2018

Answer:

Like so...

Explanation:

For example,

Basic repeating decimals

  • #0.bar(18)#

#0.bar(18)=18/99#
#color(white)(0.bar(18))=2/11#

  • #0.bar(123)#

#0.bar(123)=123/999#
#color(white)(0.bar(123))=41/333#

  • #0.bar(4680#

#0.bar(4680)=4680/9999#
#color(white)(0.bar(4680))=52/1111#

Not-so-basic repeating decimals

  • #1.0bar(42)#

Let #x=1.0bar(42)#

#1000x-10x=1042.bar(42)-10.bar(42)#
#color(white)(xxxx//)990x=1032#
#color(white)(xxxxxxx.)x=1032/990#
#color(white)(xxxxx)1.0bar(42)=1032/990#
#color(white)(xxxxx1.0bar(42))=172/165#