How do you convert repeating decimals into fractions?

1 Answer
Mar 30, 2018

Like so...

Explanation:

For example,

Basic repeating decimals

  • 0.¯¯¯¯18

0.¯¯¯¯18=1899
0.¯¯¯¯18=211

  • 0.¯¯¯¯¯¯123

0.¯¯¯¯¯¯123=123999
0.¯¯¯¯¯¯123=41333

  • 0.¯¯¯¯¯¯¯¯4680

0.¯¯¯¯¯¯¯¯4680=46809999
0.¯¯¯¯¯¯¯¯4680=521111

Not-so-basic repeating decimals

  • 1.0¯¯¯¯42

Let x=1.0¯¯¯¯42

1000x10x=1042.¯¯¯¯4210.¯¯¯¯42
××/990x=1032
×××x.x=1032990
××x1.0¯¯¯¯42=1032990
××x1.0¯¯¯¯42=172165