Question

Express each of the following decimals in the rational form ((p)/(q)). (i) 0.bar(9) (ii) 0.bar(57) (iii) 0.7bar(29) (iv) 12.2bar

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Answer 1

Answer:

(i) 1/1

(ii) 19/33

(iii) 361/495

(iv) 110/9

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Step-by-step explanation:

(i)                      

Let x =  0.9

             

10x = 9.9

                               

10x - x = 9.9 - 0.9

9x = 9

x = 1 = 1/1

(ii)                      

Let x =  0.57

                   

100x = 57.57

                                     

100x - x = 57.57 - 0.57

99x = 57

x = 57/99 = 19/33

(iii)                      

Let x =  0.729

               

10x = 7.29

                             

1000x = 729.29

                                           

1000x - 10x = 729.29 - 7.29

990x = 722

x = 722/990 = 361/495

(iv)                        

Let x =  12.2

                 

10x = 122.2

                                   

10x - x = 122.2 - 12.2

9x = 110

x = 110/9