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
1000x−10x=1042.¯¯¯¯42−10.¯¯¯¯42
××/990x=1032
×××x.x=1032990
××x1.0¯¯¯¯42=1032990
××x1.0¯¯¯¯42=172165