alvindavis99

CIP School in the Phils.

General Math: Fraction to Decimal Conversion

on August 23, 2012
Fraction to Decimal Conversion 
 

 

English: display showing fractions.

English: display showing fractions. (Photo credit: Wikipedia)

Fraction to Decimal Conversion Tables

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

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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