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Required decimal fraction = 0. 2727 ...... Required decimal fraction =
= 0. 2  7  2. 56756 ...... 2 . 567 
Conversion of Recurring Decimal into Simple Fraction
Determining the value of recurring fraction :

Example 5. Express 0. 3  into simple fraction.

Solution : 0. 3  0. 3333 ........
0. 3 u 10 0. 333 .......u 10 3. 333 ......
and 0. 3 u 1 0. 333 .......u 1 0. 333 ......

subtracting, 0. 3 u 10  0. 3 u 1 3

or, 0. 3 u  10  1 3 or 0. 3 u 9 3

Therefore,
3

1

9

3

0. 3 

Required fraction is
3

1

Example 6. Express 0. 2  4  into simple fraction.

Solution : 0. 2  4 = 0 ˜ 24242424 ........

So, 0. 2  4 u 100 0. 242424 .......u 100 24. 2424 ......

and 0. 2  4 u 1 0. 242424 .......u 1 0. 242424 ......

Subtracting 0. 2  4   100  1 24

or, 0. 2  4 u 99 24 or,
33

8

99

24

0. 2  4 

Required fraction is
33

8

Example 7. Express 5. 13  4  5 into simple fraction.

Solution : 5. 13  45  = 5. 1345345345 .........

So, 5. 13  45 u 10000 5. 1345345 ......u 10000 51345. 345 ......

and 5. 13  45 u 10 5. 1345345 .......u 10 51. 345 ......

Subtracting, 5. 13  45 u 9990 51345  51

So, 5. 13  45 =
1665

224

5

1665

8549

9990

51294

9990

51345 51