how would you convert the repeating non terminating decimal to a fraction explain the process as you solve the problem 0.1515...

Answer 1

Ms. Sue anyone help me please

Answer 2

0.1515=303\2000

Answer 3

let x = .151515...
there are 2 digits that repeat, so multiply each side by 100
(if 3 digits were to repeat, I would multiply by 1000 etc)
100x = 15.1515...
subtract the two equations
100x - x = 15.1515... - .1515...
99x = 15
x = 15/99 = 5/33

check with a calculator

If you had a case where there some non-repeating digits before the repeating digits follow the same method, but you will have to make an adjustment at the end

e.g. x = 0.23456456456...
multiply by 1000 since 3 digits repeat
1000x = 234.56456456...
again, subtract
999x = 234.330000... = 234.33
x = 234.33/999
= 23433/99900 , do you see what I just did ?
= 7811/33300

Answer 4

nonterminating decimal to a fraction