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

Question

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

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Official Answer

C

igloo · Answer

Hey hi,
10/99 = 0.101010

Hope it helps.

Posted from my month

bile device

Vips0000 · Answer

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

anon1 · Answer

VIPS YOU ARE THE MAN

booya

https://img846.imageshack.us/img846/9500/img20121105004711.jpg

Vips0000 · Answer

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..

KarishmaB · Answer

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)

Bunuel · Answer

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

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

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