0.4 repeating as a fraction




0.4 is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say 0.4 repeating, you mean that the 1 is repeating. Here is the question formulated in mathematical terms with the vinculum line above the decimal number that is repeating.

0.4 repeating as a fraction

The formula to convert any repeating decimal number to a fraction is as follows:

   
(DN x F) - NRP
 
   
D
 

DN = Decimal Number

F = 10 if one repeating number, 100 if two repeating numbers, 1000 if three repeating numbers, etc.

NRP = Non-repeating part of decimal number.

D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, etc.

Below shows you how to get the answer to 0.4 repeating as a fraction using our formula.

   
(0.4 x 10) - 0
 
   
9
 

  = 
   
4
 
   
9
 
   

Below is the answer in the simplest form possible:

0.4 repeating as a fraction
= 4/9


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