Fraction to Decimal Conversion Tables

Important Note: any span of numbers that is underlined signifies that those numbers (digits) that are repeated. For example, 0.09 signifies 0.090909... etc.

Only fractions in lowest terms are listed.  For instance, to find 2/8, first simplify it to 1/4 then search for it in the table below.
 

fraction = decimal      
1/1 = 1      
1/2 = 0.5      
1/3 = 0.3 2/3 = 0.6    
1/4 = 0.25 3/4 = 0.75    
1/5 = 0.2 2/5 = 0.4 3/5 = 0.6 4/5 = 0.8
1/6 = 0.16 5/6 = 0.83    
1/7 =  0.142857 2/7 =  0.285714 3/7 =  0.428571 4/7 =  0.571428
  5/7 =  0.714285 6/7 =  0.857142  
1/8 = 0.125 3/8 = 0.375 5/8 = 0.625 7/8 = 0.875
1/9 = 0.1 2/9 = 0.2 4/9 = 0.4 5/9 = 0.5
  7/9 = 0.7 8/9 = 0.8  
1/10 = 0.1 3/10 = 0.3 7/10 = 0.7 9/10 = 0.9
1/11 = 0.09 2/11 = 0.18 3/11 = 0.27 4/11 = 0.36
  5/11 = 0.45 6/11 = 0.54 7/11 = 0.63
  8/11 = 0.72 9/11 = 0.81 10/11 = 0.90
1/12 = 0.083 5/12 = 0.416 7/12 = 0.583 11/12 = 0.916
1/16 = 0.0625 3/16 = 0.1875  5/16 = 0.3125 7/16 = 0.4375
  11/16 = 0.6875 13/16 = 0.8125 15/16 = 0.9375
1/32 = 0.03125 3/32 = 0.09375 5/32 = 0.15625 7/32 = 0.21875
  9/32 = 0.28125 11/32 = 0.34375 13/32 = 0.40625
  15/32 = 0.46875 17/32 = 0.53125 19/32 = 0.59375
  21/32 = 0.65625 23/32 = 0.71875 25/32 = 0.78125
  27/32 = 0.84375 29/32 = 0.90625 31/32 = 0.96875

Need to convert a repeating decimal to a fraction? Follow these examples:
 

Note the following pattern for repeating decimals:
0.22222222... = 2/9
0.54545454... = 54/99
0.298298298... = 298/999
Division by 9's causes the repeating pattern.

Note the pattern if zeros precede the repeating decimal:
0.022222222... = 2/90
0.00054545454... = 54/99000
0.00298298298... = 298/99900
Adding zero's to the denominator adds zero's before the repeating decimal.

To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part.
  0.21 + 0.00456456456456456...
Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.
  21/100 + 456/99900
Now add these fraction by expressing both with a common divisor
  20979/99900 + 456/99900
and add.
  21435/99900
Finally simplify it to lowest terms
  1429/6660
and check on your calculator or with long division.
= 0.2145645645...
 
 

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