Example 1

Write 3 5 3 fifths  as a decimal.

0.6 5 3.0 Divide the numerator by the denominator. table with 2 rows and 1 column , row1 column 1 , 0.6 , row2 column 1 , 5 , long division symbol enclosing , 3.0 , end symbol , end table . cap dividethenumeratorbythedenominator.

So 3 5 = 0.6 . 3 fifths , equals 0.6 .

Example 2

Write 0.38 as a fraction.

0.38 = 38  hundredths  = 38 100 = 19 50 0.38 , equals 38 . hundredths . equals , 38 over 100 , equals , 19 over 50

Example 3

Write 3 11 3 elevenths  as a decimal.

Divide the numerator by the denominator, as shown below. The remainders 8 and 3 keep repeating. Therefore 2 and 7 will keep repeating in the quotient.

0.2727 … 11 3.0000 … 2.2 _ 80 77 _ 30 22 _ 80 77 _ 3 table with 9 rows and 1 column , row1 column 1 , table with 2 rows and 1 column , row1 column 1 , 0.2727 , dot dot dot , row2 column 1 , 11 . long division symbol enclosing , 3.0000 , dot dot dot , end symbol , end table , row2 column 1 , 2.2 with under bar below , row3 column 1 , 80 , row4 column 1 , 77 with under bar below , row5 column 1 , 30 , row6 column 1 , 22 with under bar below , row7 column 1 , 80 , row8 column 1 , 77 with under bar below , row9 column 1 , 3 , end table

3 11 = 0.2727 … = 0. 27 ¯ 3 elevenths , equals , 0.2727 , dot dot dot equals 0. , 27 bar

Example 4

Write 0.363636 … 0.363636 , dot dot dot  as a fraction.

Let x = 0.363636 … x equals , 0.363636 , dot dot dot

100 x = 36.36363636 … When  2  digits repeat, multiply by  100. 99 x = 36 Subtract  x = 0.363636. x = 36 99 , or   4 11 Divide each side by  99. table with 3 rows and 3 columns , row1 column 1 , 100 x , column 2 equals . 36.36363636 . dot dot dot , column 3 cap when , 2 . digitsrepeatcommamultiplyby . 100. , row2 column 1 , 99 x , column 2 equals 36 , column 3 cap subtract . x equals . 0.363636. , row3 column 1 , x , column 2 equals , 36 over 99 , comma or , 4 elevenths , column 3 cap divideeachsideby . 99. , end table