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Extremely embarassing, can't do long division on recurring d

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Extremely embarassing, can't do long division on recurring d [#permalink] New post   04 Nov 2012, 17:30
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Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515….
10/99 is which of the following?

0.{11}
0.{101}
0.{10}
0.{09}
0.{01}





So the answer to this is obvious (to anyone that can do long division), unfortunately I haven't done this type of LD since HS and I need a refresher.

The answer is C but I'm failing to understand why there is only 1 zero between the 1s. In the long division process we subtract 99 from 100, leaving 1. Therefore we have to add 2 zeroes to get back to 100 where we can multiply 99 into 1 again to get 100-99... but this obviously is not the case and I'm struggling to understand why.

Can anyone help me out? I've attached a picture of my work...

Thank you so much guys



OPEN DISCUSSION OF THIS QUESTION IS HERE: curly-brackets-around-the-last-digits-of-a-decimal-fraction-signify-229602.html



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C
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igloo
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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   04 Nov 2012, 19:55
Hey hi,
10/99 = 0.101010

Hope it helps.

Posted from my month


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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   04 Nov 2012, 22:20
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anon1 wrote:
Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515….
10/99 is which of the following?
0.{11}
0.{101}
0.{10}
0.{09}
0.{01}
So the answer to this is obvious (to anyone that can do long division), unfortunately I haven't done this type of LD since HS and I need a refresher.
The answer is C but I'm failing to understand why there is only 1 zero between the 1s. In the long division process we subtract 99 from 100, leaving 1. Therefore we have to add 2 zeroes to get back to 100 where we can multiply 99 into 1 again to get 100-99... but this obviously is not the case and I'm struggling to understand why.
Can anyone help me out? I've attached a picture of my work...
Thank you so much guys


The problem in your division is, that you forgot that you had added decimal already and what is its effect.

Try dividing this first: 100000/99
And then come back and try dividing 10.0000/99
Compare these 2 calculations (specially the second one to your calculation)

Hopefully you'll see the underlying concept and results ;)
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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   04 Nov 2012, 22:50
VIPS YOU ARE THE MAN

booya

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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   04 Nov 2012, 23:12
anon1 wrote:
VIPS YOU ARE THE MAN

booya


ha ha.. glad it helped..
here is another trick to avoid such lengthy calculation

if u divide a number N by 9s (k times 9), it always gives the same repeating numbers .(0000) N (0000) N
(0000) depends on how many 9s are there.

eg:
2/9 = 0.222222222....
5/99 = 0.0505050505....
10/99= 0.1010101...
111/999=0.111111111..

and so on.. ;)
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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   06 Nov 2012, 00:30
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anon1 wrote:
Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515….
10/99 is which of the following?

0.{11}
0.{101}
0.{10}
0.{09}
0.{01}





So the answer to this is obvious (to anyone that can do long division), unfortunately I haven't done this type of LD since HS and I need a refresher.

The answer is C but I'm failing to understand why there is only 1 zero between the 1s. In the long division process we subtract 99 from 100, leaving 1. Therefore we have to add 2 zeroes to get back to 100 where we can multiply 99 into 1 again to get 100-99... but this obviously is not the case and I'm struggling to understand why.

Can anyone help me out? I've attached a picture of my work...

Thank you so much guys



You may want to check out khanacademy.org

It has great videos to explain a lot of basic concepts. Here is the link that teaches you long division:

https://www.khanacademy.org/math/arithme ... 4-division

Another great basic concept website is purplemath.com (for algebra)
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Re: Extremely embarassing, can't do long division on recurring d [#permalink] New post   12 Apr 2017, 00:50
Expert Reply
anon1 wrote:
Curly brackets {} around the last digits of a decimal fraction signify that these digits recur an infinite number of times. For example 0.1{5} is a shorthand for 0.1555555… Similarly, 0.{15} is a shorthand for 0.15151515….
10/99 is which of the following?

0.{11}
0.{101}
0.{10}
0.{09}
0.{01}





So the answer to this is obvious (to anyone that can do long division), unfortunately I haven't done this type of LD since HS and I need a refresher.

The answer is C but I'm failing to understand why there is only 1 zero between the 1s. In the long division process we subtract 99 from 100, leaving 1. Therefore we have to add 2 zeroes to get back to 100 where we can multiply 99 into 1 again to get 100-99... but this obviously is not the case and I'm struggling to understand why.

Can anyone help me out? I've attached a picture of my work...

Thank you so much guys



OPEN DISCUSSION OF THIS QUESTION IS HERE: curly-brackets-around-the-last-digits-of-a-decimal-fraction-signify-229602.html



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: Extremely embarassing, can't do long division on recurring d [#permalink]
12 Apr 2017, 00:50
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