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Fraction to Decimal Conversion Tables

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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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