i don't get how to do this problem mrs. sue please help

Question

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?

Answer 1

http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/conv_rep_decimals/v/coverting-repeating-decimals-to-fractions-1

Answer 2

for the second part i don't get how to convince that the number 0.57 is a rational number please help me

Answer 3

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

Answer 4

thanks