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Number (Higher) - Changing a Recurring Decimal to a Fraction
 
Examples
 
Examples

This is a common question on the Higher paper and requires good preparation.

Example 1: Change 1.7777… to a fraction.

Method:
Let x = 1.7 then
10x
=
 17.7 and subtracting gives
   
9x
=
 16  
   
x
=
 16/9  
   
x
=
 1
 7
9		  


Example 2: Change 0.3232323232… to a fraction.

Let x = 0.32323232…(Because there are two figures recurring, multiply by 100).
100x =
  
32.323232…
    
x =
  
0.323232…
   (subtracting)
99x =
   32    
x =
   32/99    


Example 3: Change 0.084848484… to a fraction.

(Note: the 0 is not recurring).
 1000x
=
84
 .848484…   (x1000 to move the point)
  10x
=
0
 .848484…   (x10 to move the point)
990x
=
84
     (subtracting)
x
=
84
      
   
990
     (cancel)
x
=
14
      
   
165