# How do you convert repeating decimals into fractions?

##### 1 Answer

Mar 30, 2018

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#