CONVERTING FRACTIONS TO REPEATING DECIMALS

One way to convert fractions to decimals in situations in which the period is greater than the standard number of digits displayed on a calculator or computer is to use a spreadsheet.

Here, in a table, are the formulas I used ( in Excel ). Please read the notes at the end.

  A B C D E F
1 input denominator =3^5      
2            
3 numerator denominator

decimal digit

      
4 =1 =C1 =INT(10*A4/B4) =10*A4-B4*C4 see note (2) see note (3)
5 =D4 =B4 =INT(10*A5/B5) =10*A5-B5*C5    
6 =D5 =B5 =INT(10*A6/B6) =10*A6-B6*C6    
7  see note (1)          

(1) for columns A, B, C and D, copy and repeat the formulas for as many rows as you think necessary depending on the length of the period of the decimal equivalent of the fraction you are converting.

(2) the decimal digits in column C were combined in groups using the formula C4&C5&C6&C7 etc. for about 20 rows (your choice)

(3) the groups of digits collected in certain cells of column D were gathered together : =CONCATENTATE(E4,E24,E44,..........)  ; if the period was extremely long I might break up into more than one CONCATENTATE formula in cells beneath each other in an attempt to get the results to print out on a single sheet of paper. For example, the following is the decimal expansion of 1/7^3. Can you find the period ? What is its length ? Are there any interesting patterns ?

002915451895043731778425655976676384839650145772594752186588921282798833819241982507288629737609329446064139

941690962099125364431486880466472303206997084548104956268221574344023323615160349854227405247813411078717201

166180758017492711370262390670553935860058309037900874635568513119533527696793002915451895043731778425655976

676384839650145772594752186588921282798833819241982507288629737609329446064139941690962099125364431486880466

472303206997084548104956268221574344023323615160349854227405247813411078717201166180758017492711370262390670

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