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trick to convert recurring decimals to fraction

Expert replies
by abhi332 » Mon Feb 22, 2010 12:32 pm
Few tricks

1) 0.6666...

to convert 0.6666... to fraction, we know 6 is repeated every time.i.e there is only 1 digit repetition so I will divide 6 by single digit 9

so, i can write it as 6/9

2) 0.46464646...

here 46 is repeated so there are 2 digits

fraction is 46/99

3)0.23434343434...

here we can see that after 0.2 , 34 is repeated
fraction = ( decimal - non repeated decimal)/(9 digits equal to no of repeated decimals * 10^(no of non repeated decimal))

looks complicated, but it is actually not ;-)

fraction = (234 - 2)/(99 * 10^1) = 232/990

4)0.1234343434.....

fraction = (1234-12)/(99 * 10^2) = 1222/9900

[/list]
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Source: — Problem Solving |

by harsh.champ » Tue Feb 23, 2010 2:25 am
Alternatively,



1) 0.6666...

0.111 =1/9
0.222...= 2 x 1/9
0.3333.... = 3 x 1/9
So on and so forth.


2) 0.46464646...

x=0.464646
100x = 46.464646(if 3 digit were repeating multiply by 10^3;if n digits repeat multiply by 10^n)
Subtracting x from 100x
99x = 46
so, x =46/99


3)0.23434343434...

x = 0.234343434...
10x = 2.34343434
[2(n) digits repeating,multiplying by 10^n or 10^2]
1000x = 234.343434
990x = 232
x=232/990
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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