Time remaining:
what is this number as a fraction? show work

Mathematics
Tutor: None Selected Time limit: 0 Hours

1.2444444444444444444444444444444444444444444444444444444444 and so on

Oct 2nd, 2014

1.24444444444444444444444444444444444...

= 1.2 + 0.44444444444444444444444444444...

= 6/5 + 0.44444444444444444444444444444... (*)

Now 0.44444444444444444444444444444... = 4/10 + 4/ 100 + 4/1000 + ,,, is a geometric series with 

a= 0.4 and r = 0.1 and has sum to infinity = a/ (1 -r ) 

                                                                   = 0.4/ ( 1- 0.1)

                                                                   =  0.4/ 0.9

                                                                   = 4/9          

Hence the required fraction  from (*)   = 6/5 + 4/9 = 54/45 + 20/45 = 74/45       

Oct 2nd, 2014

Are you studying on the go? Check out our FREE app and post questions on the fly!
Download on the
App Store
...
Oct 2nd, 2014
...
Oct 2nd, 2014
Dec 8th, 2016
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer