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# Decimals to fractions Tweet

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1. Re: Decimals to fractions
(Original post by raheem94)
I will do it this way,
Spoiler:
Show

Using the sum to infinity formula,

Sorry, but your method lacks elegance.
Attached Thumbnails

2. Re: Decimals to fractions
(Original post by steve2005)
Sorry, but your method lacks elegance.
Fair enough.
3. Re: Decimals to fractions
(Original post by steve2005)
0.333333333 times 3 is 0.999999999999 . What justification do you have for saying 0.9999999999..... equals 1

The method I used allows for the decimal part to cancel.
(Original post by steve2005)
A question for you.

Change 1.346346346..... into a fraction.
EDIT: I understand what you mean - assuming that 0.999...=1 is basically assuming how to write 0.999... as a fraction, and what we're trying to do is represent decimals as fractions So I guess it would be an inappropriate assumption!

Makes sense. I'd just assume that 0.999...=1 or that 3.999...=4 because I know that it is true- I wouldn't usually justify rigourously every single assumption I make. I guess that does only work with simple ones though

How would you solve that one (elegantly )?

Last edited by Implication; 17-05-2012 at 10:01.
4. Re: Decimals to fractions
(Original post by Implication)
EDIT: I understand what you mean - assuming that 0.999...=1 is basically assuming how to write 0.999... as a fraction, and what we're trying to do is represent decimals as fractions So I guess it would be an inappropriate assumption!
Well if you're going to say 0.9r = 1 then prove it using x = 0.9r then 10x = 9.9r you might as well use that method to begin with

And yes that is how you would solve it.
5. Re: Decimals to fractions
(Original post by raheem94)
I will do it this way,
Spoiler:
Show

Using the sum to infinity formula,

While this isn't really as neat/easy as the method you used before (10x = ..) it was an interesting way to go about it I liked that haha.
6. Re: Decimals to fractions
(Original post by hassi94)
While this isn't really as neat/easy as the method you used before (10x = ..) it was an interesting way to go about it I liked that haha.
If you are given this question, which method will you use?

Do you have a different method to solve it?
7. Re: Decimals to fractions
(Original post by raheem94)
If you are given this question, which method will you use?

Do you have a different method to solve it?
I'd have done what Steve2005 did (as I was taught it at GCSE and it seems the most sensible way round it and the method that sticks in my head).
8. Re: Decimals to fractions
(Original post by Implication)
EDIT: I understand what you mean - assuming that 0.999...=1 is basically assuming how to write 0.999... as a fraction, and what we're trying to do is represent decimals as fractions So I guess it would be an inappropriate assumption!

Makes sense. I'd just assume that 0.999...=1 or that 3.999...=4 because I know that it is true- I wouldn't usually justify rigourously every single assumption I make. I guess that does only work with simple ones though

How would you solve that one (elegantly )?

Yes, that's what I would do.

I think it's neat .
9. Re: Decimals to fractions
(Original post by steve2005)
Yes, that's what I would do.

I think it's neat .
Do you know about any other method, other than mine and yours, to solve this question?