## anonymous 4 years ago Solve the problem.

1. anonymous

$6\overline{.25}= P/Q$

2. 2bornot2b

Do you want to express 6.25252525..........as P/Q, where P and Q are coprimes?

3. anonymous

yes i do want to express it like that... and it just shows it like that on my paper p/q as a fraction.

4. 2bornot2b

First I say let x = 6.252525........... Now I multiply both sides by 10^4

5. 2bornot2b

(10^4)x=62525.2525...

6. anonymous

On my homework it says to multiply it by a hundred or that is what my teacher told me.

7. 2bornot2b

You may do that, it doesn't matter

8. 2bornot2b

Say at first you multiply by 100, then multiply by 10 In my problem I am first multiplying by 10000, and then by 1000

9. anonymous

Oh well i am not sure how that is why i posted it on here haha.

10. 2bornot2b

what do you mean by "Oh well i am not sure how that is"

11. 2bornot2b

Any way, since I see you are already familiar with the procedure. I am stating it once again, in a better way, so that you understand the thing better.

12. anonymous

I am not sure how to multiply it by a 100 like i don't know how to solve it.

13. 2bornot2b

STEP 1. Assume x = (the number given to you)

14. 2bornot2b

STEP 2. Multiply both sides by 10^n

15. 2bornot2b

STEP 3: Multiply both sides by 10^m

16. 2bornot2b

So now you have two equations (Not m must be lesser than n)

17. 2bornot2b

Subtract the second equation from the first

18. 2bornot2b

Now you will get a good equation which looks like P/Q

19. 2bornot2b

I am solving the problem given by you....

20. anonymous

yes i know.

21. 2bornot2b

|dw:1327088110491:dw|

22. anonymous

now what do i do after this doesnt it have to be turned into an equation.

23. 2bornot2b

|dw:1327088136907:dw|

24. 2bornot2b

|dw:1327088233575:dw|

25. 2bornot2b

|dw:1327088285898:dw|

26. 2bornot2b

|dw:1327088337495:dw|

27. 2bornot2b

So I have expressed x as P/Q, and x is equal to 6.2525...

28. 2bornot2b

Did you understand?

29. anonymous

So the last part is p/q? And yes for the most part i did.

30. 2bornot2b

Of course, the last part is p/q

31. 2bornot2b

However, you must simplify that, to get the actual p and q

32. anonymous

alright just making sure... so it does not need to be reduced

33. 2bornot2b

Yes, you need to reduce ofcourse

34. anonymous

alright

35. 2bornot2b

You can't leave it there. I just expressed x equal to some p/q. But as you can see, p and q has common factors. So you need to cancel and come to a point, where p and q can't be cancelled any further

36. 2bornot2b

Take a look at page 14 (example 5) of this book http://books.google.co.in/books?id=SnvBeodeTDcC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

37. 2bornot2b

A similar problem is solved there