Solve the problem.

- anonymous

Solve the problem.

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- anonymous

\[6\overline{.25}= P/Q\]

- 2bornot2b

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

- 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.

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## More answers

- 2bornot2b

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

- 2bornot2b

(10^4)x=62525.2525...

- anonymous

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

- 2bornot2b

You may do that, it doesn't matter

- 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

- anonymous

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

- 2bornot2b

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

- 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.

- anonymous

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

- 2bornot2b

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

- 2bornot2b

STEP 2. Multiply both sides by 10^n

- 2bornot2b

STEP 3: Multiply both sides by 10^m

- 2bornot2b

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

- 2bornot2b

Subtract the second equation from the first

- 2bornot2b

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

- 2bornot2b

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

- anonymous

yes i know.

- 2bornot2b

|dw:1327088110491:dw|

- anonymous

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

- 2bornot2b

|dw:1327088136907:dw|

- 2bornot2b

|dw:1327088233575:dw|

- 2bornot2b

|dw:1327088285898:dw|

- 2bornot2b

|dw:1327088337495:dw|

- 2bornot2b

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

- 2bornot2b

Did you understand?

- anonymous

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

- 2bornot2b

Of course, the last part is p/q

- 2bornot2b

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

- anonymous

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

- 2bornot2b

Yes, you need to reduce ofcourse

- anonymous

alright

- 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

- 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

- 2bornot2b

A similar problem is solved there

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