Asked by kathy
                i don't get how to do this problem mrs. sue please help 
how would you convert the repating nonterminating decimal to a fraction? explain the process as you solve the problem/0.1515... remember to show all of the steps that you use to solve the problem
how would you convince a fellow student that the number 0.57 is a rational number?
            
        how would you convert the repating nonterminating decimal to a fraction? explain the process as you solve the problem/0.1515... remember to show all of the steps that you use to solve the problem
how would you convince a fellow student that the number 0.57 is a rational number?
Answers
                    Answered by
            Ms. Sue
            
    http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/conv_rep_decimals/v/coverting-repeating-decimals-to-fractions-1
    
                    Answered by
            kathy
            
    for the second part i don't get how to convince that the number 0.57 is a rational number please help me 
    
                    Answered by
            Reiny
            
    What Sal is basically showing you in the video is this:
look at the repeating decimal places , there are 2 digits in the repeating loop
so, let
x = .151515...
because we have 2 digits repeating, let's multiply the equation by 100
100x = 15,151515...
notice the decimal part of 100x looks the same as the decimal part of x
so if we subtract the two equations we get
100x = 15.151515...
x = .1515151...
----------------
99x = 15
divide by 99
x = 15/99 which reduces to 5/33
Use your calculator to divide 5 by 33 and see what you get
In the above method , if there had been 3 digits repeating, then I would have multiplied by 1000 etc
For .57 , since there are no repeating decimals (well, I guess we can say .5700000.... )
the result is simply 57/100 by definition
and 57/100 is surely a fraction, thus rational
    
look at the repeating decimal places , there are 2 digits in the repeating loop
so, let
x = .151515...
because we have 2 digits repeating, let's multiply the equation by 100
100x = 15,151515...
notice the decimal part of 100x looks the same as the decimal part of x
so if we subtract the two equations we get
100x = 15.151515...
x = .1515151...
----------------
99x = 15
divide by 99
x = 15/99 which reduces to 5/33
Use your calculator to divide 5 by 33 and see what you get
In the above method , if there had been 3 digits repeating, then I would have multiplied by 1000 etc
For .57 , since there are no repeating decimals (well, I guess we can say .5700000.... )
the result is simply 57/100 by definition
and 57/100 is surely a fraction, thus rational
                    Answered by
            kathy
            
    thanks
    
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