Author Topic: Help with finals  (Read 775 times)

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Offline MicroFox01

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Help with finals
« on: June 02, 2015, 08:44:06 pm »
     my math teacher gave us a sheet and said this will be on you final.... and this one question was impossible, if anyone can explain how it works I thank you in advance cause like I said it was impossible. write 1/4 as a repeating decimal

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Re: Help with finals
« Reply #1 on: June 03, 2015, 10:51:50 am »
Sorry to say this, but I do believe 'repeating' decimal would be innapropriate in this case, as 1/4 cannot be written as such, one quarter (1/4) is simply 0.25 (100 divided by 4, then divided by ten). Just remember, 1/3=0.333333333333 etc, 1/2=0.5, 1/5=0.2. If you ever need to write a fraction as a repeating decimal, it will usually be ?/9, ??/99, or ???/999, to which if it is for example, 435/999, as a decimal that would be 0.435435435435 etc, and if it were say, 25/33 you would multiply by three to get 75/99, and therefore 0.757575 etc. anything you dont understand please ask i will be happy to help ^,^
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Offline Amelia

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Re: Help with finals
« Reply #2 on: June 03, 2015, 10:55:29 am »
One quarter is a rational number with a terminating decimal (0.25) there's no way to write it as a repeating decimal.. Maybe you should talk to your teacher, it could have been a typo or mistake and they'll fix it. Good luck with the rest of your final!
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Re: Help with finals
« Reply #3 on: June 03, 2015, 11:29:10 am »
Yeah, it's physically impossible to write 1/4 as a repeating decimal, unless if maybe 0.25000... was the answer. Wait no never mind. By definition, 0.25 is a terminating decimal, and therefore never could be a repeating decimal as the only number that could appear after the .25 is 0, not the 25 that is needed to make it repeating.

What I think is going on is that the teacher is asking an impossible question on purpose. You can ask if it's a mistake, but I believe that what you're supposed to do is explain in detail why this question is impossible to correctly answer. Even if it's not what you should do, it's worth a shot and could earn maybe a B or C instead of a total 0.

I think the question was made to catch any student that really wasn't paying attention in class, because if they didn't pay attention they'd just write 0.25 and move on with life.
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Offline JJ Husky / James

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Re: Help with finals
« Reply #4 on: June 03, 2015, 11:47:58 am »
You guys over in merca get asked trick questions? 0.o
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Re: Help with finals
« Reply #5 on: June 03, 2015, 11:52:41 am »
You guys over in merca get asked trick questions? 0.o

Only certain teachers who suck do!

My teachers were stabdup people. They were not only my teachers, they were my close friends too and they know more about my personal life than my family ^-^"

But not all teachers are like that.

For example the teacher mentioned in the OP.
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Re: Help with finals
« Reply #6 on: June 03, 2015, 12:04:07 pm »
You guys over in merca get asked trick questions? 0.o
I live in Canada and they don't always do trick questions but they make really good test questions. They test you knowledge and understanding to make sure you know th concepts instead of just memorizing a procedure
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Re: Help with finals
« Reply #7 on: June 03, 2015, 08:48:28 pm »
Finally, something I can help with!

First off, it IS possible to write 1/4 as a repeating decimal. To do this, you first should know this,

1/3 = 0.333333 (repeat forever) (I will now use three dots to show that a decimal goes forever.)

continued...

1/3 + 1/3 + 1/3 = 1

By changing all the fractions to their decimal counterpart, we get

0.333... + 0.333... + 0.333... = 0.999999...

But how can this be? How can the same question get two answers?
Well you cant get two for the price of one, that's why 0.999.... IS equal to one.

So now that we know 0.9999... is equal to 1 we can do this,

1/4 = 0.25 and  0.00999... = 0.01

Subtract 0.01 from 0.25, you get 0.24.

Then, add 0.00999... to 0.24

You get 0.2499999...
This equals 0.25 and also 1/4

Tah da! You now have a decimal that equals 1/4 and is repeating! Hope this helped!
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Re: Help with finals
« Reply #8 on: June 03, 2015, 11:34:11 pm »
Finally, something I can help with!

First off, it IS possible to write 1/4 as a repeating decimal. To do this, you first should know this,

1/3 = 0.333333 (repeat forever) (I will now use three dots to show that a decimal goes forever.)

continued...

1/3 + 1/3 + 1/3 = 1

By changing all the fractions to their decimal counterpart, we get

0.333... + 0.333... + 0.333... = 0.999999...

But how can this be? How can the same question get two answers?
Well you cant get two for the price of one, that's why 0.999.... IS equal to one.

So now that we know 0.9999... is equal to 1 we can do this,

1/4 = 0.25 and  0.00999... = 0.01

Subtract 0.01 from 0.25, you get 0.24.

Then, add 0.00999... to 0.24

You get 0.2499999...
This equals 0.25 and also 1/4

Tah da! You now have a decimal that equals 1/4 and is repeating! Hope this helped!

Sadly, this work doesn't check out.

A repeating decimal is repeating the whole time. Unless if it repeats the 24, it by definition isn't repeating.

However, maybe...

If we repeated the 24 at a point where it would have no impact on the end result...

What about 0.2499999924999999? Add more 9's if necessary, but make sure you have the same amount of 9's after both 24.

Do you all think that'd work?
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Re: Help with finals
« Reply #9 on: June 04, 2015, 12:08:06 am »
Finally, something I can help with!

First off, it IS possible to write 1/4 as a repeating decimal. To do this, you first should know this,

1/3 = 0.333333 (repeat forever) (I will now use three dots to show that a decimal goes forever.)

continued...

1/3 + 1/3 + 1/3 = 1

By changing all the fractions to their decimal counterpart, we get

0.333... + 0.333... + 0.333... = 0.999999...

But how can this be? How can the same question get two answers?
Well you cant get two for the price of one, that's why 0.999.... IS equal to one.

So now that we know 0.9999... is equal to 1 we can do this,

1/4 = 0.25 and  0.00999... = 0.01

Subtract 0.01 from 0.25, you get 0.24.

Then, add 0.00999... to 0.24

You get 0.2499999...
This equals 0.25 and also 1/4

Tah da! You now have a decimal that equals 1/4 and is repeating! Hope this helped!

Sadly, this work doesn't check out.

A repeating decimal is repeating the whole time. Unless if it repeats the 24, it by definition isn't repeating.

However, maybe...

If we repeated the 24 at a point where it would have no impact on the end result...

What about 0.2499999924999999? Add more 9's if necessary, but make sure you have the same amount of 9's after both 24.

Do you all think that'd work?

Actually, according to all the examples I've searched up, a repeating decimal doesn't need to repeat all the numbers in it the decimal, but rather a certain portion of the end just needs to repeat. https://www.mathsisfun.com/definitions/recurring-decimal.html This site includes the example of 77/600 or 0.1283333... This decimal does not repeat the beginning, but does infinitely repeat the 3, earning it name of repeating decimal. Going off this example and the definition, 0.24999... would be viable as a repeating decimal and would be able to answer Micro's question.
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