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

Herc
Ms. Sue anyone help me please

davonte
0.1515=303\2000

Reiny
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 nonrepeating 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
Respond to this Question
Similar Questions

Math
Can someone help me with this problem? A) Separate the fractions 2/6, 2/5, 6/13, 1/25, 7/8, and 9/29 into two categories: those that can be written as a terminating decimal and those of nonterminating. Write an explanation of how 
6th grade math
Please check to make sure I did these correctly, so confusing. Thank you. Rename each fraction as a terminating or repeating decimal 13/20 .65 1/3 0.3333333333333333 2/9 0.2222222222222222 5/12 0.4166666666666667 1/16 0.0625 Rename … 
pre algebra help
9. how you would convert the repeating, non terminating decimal to a fraction? 
math
how would you convert the repating nonterminating decimal to a fraction? 
math
i don't get how to do this problem mrs. sue please help how would you convert the repating nonterminating decimal to a fraction? 
algebra
i need you to check my answers for the following questions: use the table to answer problems 1 to 4. the table lists the commuting times for 5 people. write each ratio in the form a/b, and then as a decimal. tell whether each decimal … 
math
How would you convert the repeating nontermonating decimal to a fraction? 
Math
9. how you would convert the repeating, non terminating decimal to a fraction? 
math
Tell me whether each fraction. 1/n, is given as a terminating decimal or a repeating decimal for the given rules of n. Write t for terminating or r for repeating. It starts at 2 10 which are t and r. 
Math
Using vocabulary terminating non terminating repeating non repeating explain why the value 3.14is rational while the value for pie is irrational