## JokerSmart one year ago ___ What is 0.12 expressed as the quotient of two integers in simplest form?

1. JokerSmart

$\frac{ 3 }{ 25 }$ I believe.

2. mathstudent55

This is how I learned to find a fraction for a repeating, non-terminating decimal. I'll show it to you step by step.

3. JokerSmart

Thank you for taking the time to help me out. ^_^

4. mathstudent55

Call the number x, and write the number leaving space above it, like this: |dw:1432836892783:dw|

5. mathstudent55

Sorry, it's better like this, leaving room to the left of the number, too. |dw:1432836947882:dw|

6. mathstudent55

Since there are 2 repeating decimal places, 0.1212..., we need 10^2. You always use 10 to the power that is the number off repeating decimals. 10^2 = 100, so we multiply both sides by 100 and write the new equation above the original equation: |dw:1432837075824:dw|

7. mathstudent55

Do you follow so far?

8. JokerSmart

Ah that's right! I think I have something similar like that in my notes.

9. mathstudent55

Now you subtract the bottom equation from the top equation, like this: |dw:1432837224992:dw|

10. mathstudent55

Since 99x = 12, we simply divide both sides by 99 and reduce. |dw:1432837294475:dw|

11. mathstudent55

The answer is $$\dfrac{4}{33}$$

12. JokerSmart

So 12.121212 - 0.121212 = 12 I see. Ah thank you so much. I should probably write this down for future reference. xD I appreciate your help! I as a bit off from the answer, haha

13. mathstudent55

Now notice why your answer above is incorrect. |dw:1432837370538:dw|

14. JokerSmart

Yeah, I missed something around there.

15. mathstudent55

Your answer was for the terminating, non-repeating decimal 0.12 The question is about the repeating, non-terminating decimal 0.121212... They are different numbers. The non-terminating one is a little larger than the terminating one.