4.205 repeating as a fraction




4.205 is a repeating decimal number and you want to convert it to a fraction or mixed number. When you say 4.205 repeating, you could mean that 5, 05, or 205 is repeating.

Thus, there are three different ways of answering "What is 4.205 repeating as a fraction?" Here are the three questions formulated in mathematical terms with the vinculum line above the decimal numbers that are repeating.

4.205 repeating as a fraction
4.205 repeating as a fraction
4.205 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 each of the three different questions above using our formula.



4.205 repeating as a fraction

   
(4.205 x 10) - 4.20
 
   
9
 

  = 
   
37.85
 
   
9
 
  = 
   
3785
 
   
900
 
   

Below is the answer in the simplest form possible:

4.205 repeating as a fraction
= 4 37/180



4.205 repeating as a fraction

   
(4.205 x 100) - 4.2
 
   
99
 

  = 
   
416.3
 
   
99
 
  = 
   
4163
 
   
990
 
   

Below is the answer in the simplest form possible:

4.205 repeating as a fraction
= 4 203/990



4.205 repeating as a fraction

   
(4.205 x 1000) - 4
 
   
999
 

  = 
   
4201
 
   
999
 
   

Below is the answer in the simplest form possible:

4.205 repeating as a fraction
= 4 205/999




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4.206 repeating as a fraction
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