5/7/12 - 7:59pm

- illiniPride
- |1,171
- | Rank: King Kong

- CS
- Corporate Strategy - Manager

As penance for liberally beating a dead goat in the other Brainteaser thread, here is a fresh one that should be easy for many of you:

Does .9 repeated = 1?

Please prove mathematically and explain in English. SB for the first to do both.

Popular Content

- Ask Natalie from Accepted about Business School AdmissionsWSO is excited to have the experts from Accepted on board to answer applicant questions in the business school forum. Here are messages from Natalie and Jen who will be checking this thread every few days: Natalie I'm here to answer any questions you have regarding Business School...
- Every Second Counts**Disclaimer**: *This is not a stupid self help post, just something I thought people should know. I am quite shit at helping others personally in general so don't expect much or in fact anything.* What I have to say It goes like this, I have changed jobs recently and have had less...
- What It Really Means to Be "Alpha"I'm fairly new here, and deciding what to write about in a blog entry might seem easy enough, but I'd rather people enjoy what I read than just read it and forget it. So I spent some time this week going through the more popular posts on WSO, and a good chunk of them revolve around...
- Take offer in diff city to get over a girl?It was the summer of 2014 when I first met her. We were both interning in the city; she was a year older and I met her when my friend, who was her roommate of 2 years, introduced us at a bar. Initially, I wanted to get to know her better so she could help me get a job – I wanted to line up an...
- How NOT to NetworkFollowing up after an info session is great, especially if you actually took some positive information from it.... However, there is a new email circulating Wall Street that may not dethrone the "Barclays Welcome to the Jungle" one from a few years back but.... here is some...
- New WSO Podcast Launched! Subscribe TodayHey WSO Community - we're super excited to (finally) announce the launch of the Wall Street Oasis Podcast!!! The Wall Street Oasis podcast offers the same trusted content you love from the site with even deeper access to the most interesting people in the world of finance. Talking with...
- CFA Charterholder who left finance and joined the Army—AMATitle explains it. I’m Alex Cook, and you might have seen my YouTube video on the CFA Program. I can't post links here right now but it will pop up if you type in "How I passed all of the CFA Program exams." The military has been something that I have always really thought...
- Man dragged off United flightMany of you guys probably already saw the video from last night of a man being dragged through the aisle of the United plane because it was overbooked. He was randomly selected to get bumped to the next flight and, after refusing, was carried out by security. United issued the...
- Asian name on resume I am an international student and a rising junior at a semi-target/low target school. When crafting my resume, is it advisable for me to create an English name (the likes of John/Dan) to fend off xenophobia? Or should I just go by my real name, which all of my friends and previous employers...
- Wall Street vs. Entrepreneurship I am very new to this but I thought I would post something I feel many of us students have thought about at some point in time. This may be more tailored to first-gen, low-income, students who attend non-targets. Can apply to others as well so feel free to critique? You spend hours at school,...

Forum Topics

- Consulting profile chancesCandidate Profile: -non-target big ten state school in the midwest -Junior (Graduating Spring 2018) -Double major in Finance and Economics -3.8 cumulative GPA, 3.9 Econ GPA, 4.0 finance GPA -Previous...
- Is IU Kelley overrated?I've been researching a lot about Kelley lately and I'm starting to think it is overrated. For starters, they are a huge business school, so the argument that they place 50 to 60 kids in IB means...
- WSO Internships & Employment OpportunitiesJoin the Wall Street Oasis Team OPEN OPPORTUNITIES FOR STUDENTS*: < ul> Blogging Internship *Top interns in these programs will be considered for management level internships and/or...
- S&T/global markets Superday Interview for Summer I was wondering what types of questions are typical for Summer analyst roles in markets/s&T? also wondering if its any different for french banks? First round was entirely fit, I assume superday...
- Citadel vs Goldman Sachs offer adviceI have job offers as a client facing quant from Goldman Sachs and as an execution trader at Citadel market making. Which offer should i take?
- DCF - Terminal Value Issue Hi, I need some help with my DCF in calculating the terminal value. When using perpetuity growth rate, my share price is in reasonable range. However, alternatively, when I use NOPAT/WACC to...
- How to take good notesAnyone have any tips about how to get down all important details in a meeting that might last several hours? I find it really hard to concentrate for that period of time, and sometimes notice my...
- M&A / PE post 30?I'm wondering how easy it will be to switch careers at 32. In short, I have 7 years' experience in Corporate Strategy (mainly operational, i.e. product strategy etc, no real deal / M&A focus),...
- I've been handed the Holy Grail of Opportunities...A mutual friend has said he'll place my resume directly on the desk of one the largest WM firms out there. However, unlike many people here, I don't have the degree- nor the credentials. I have...
- IU Kelly plus Honors college?Hi! I am a current senior in high school and am thinking about attending IU in the fall. I am direct admit to Kelly and to the honors college (Hutton). I would probably plan on majoring in Finance. I...
- WSO Contest 4/6/17 - Win a free WSO T-Shirt! Enter yourself in the Rafflecopter contest for a chance to win a free WSO shirt.a Rafflecopter giveaway To enter, just follow the instructions via Rafflecopter. It involves visiting us on facebook (...
- Disliking Nieces and NephewsI don't know if I've ever actually started a thread. These days, I'm not especially active, and when I am, I'm either inebriated and writing something snarky or sober and writing something too long...
- Growth Equity InterviewAny advice on preparing for a growth equity interview / typical questions? I have one coming up but there are very slim details on WSO compared to traditional LBO opportunities.
- Getting into PE, VC out of StanfordI'll be a Management Science and Engineering Major at Stanford starting this fall. I'm interested in the combo between tech and finance. I am not really the entrepreneurial-type person that would...
- Most practical valuation book?Wanted to get WSO's opinion on which valuation book (Rosenbaums, Damodaran, McKinsey, TTS etc.) is the best from a practical perspective. Basically, I'd like to work on my knowledge of corporate...

- Apr 19 2017 (All day) to Apr 20 2017 (All day)
- Apr 19 2017 (All day)
- Apr 20 2017 (All day) to Apr 21 2017 (All day)
- Apr 23 2017 - 7:00pm to 8:00pm
- Apr 24 2017 (All day) to Apr 25 2017 (All day)

## Comments (43)

A Geometric series is probably easier.

## Want to Vote on this Content?! No WSO Credits ?

just construct a cauchy sequence

## Want to Vote on this Content?! No WSO Credits ?

No.

## Want to Vote on this Content?! No WSO Credits ?

You can explain this without any fancy math, using the definition of numbers alone.

## Want to Vote on this Content?! No WSO Credits ?

x = 0.9

10x = 9.9

10x - x = 9

GBS

## Want to Vote on this Content?! No WSO Credits ?

.9 repeated has a limit value of 1, but is never actually 1.

## Want to Vote on this Content?! No WSO Credits ?

If abs (x) <1, the infinite series sum(x^n) converges to 1/(1-x)

let x = (1/10)

finite sum = 1/(1-.1)

this gives you 1 + .1 + .01 + .001 ....

subtracting 1 and multiplying by 9 gives you .9 + .09 + .090 ....

solution = [1/(1-.1) -1] *9 = [10/9 - 9/9] * 9 = 1

## Want to Vote on this Content?! No WSO Credits ?

This statement makes no sense at it stands. If you mean to say constructing a sequence where each additional term is made by appending another 9, then yes, this sequence has a limit of 1. If you mean the number .9 repeating, well, it's a constant, so its "limit value" must be itself. By the way, that is most definitely 1.

## Want to Vote on this Content?! No WSO Credits ?

x = 0.9

10x = 9.9

10x - x = 9

9x = 9

x = 1

## Want to Vote on this Content?! No WSO Credits ?

.

## Want to Vote on this Content?! No WSO Credits ?

Because an infinite string of 0.9 will always equal 1? There is no number between 0.9 repeating and 1; they are the same number, represented differently.

0.25 = 0.24(9) repeating

## Want to Vote on this Content?! No WSO Credits ?

I don't think your answer is correct.

10*.9=9

not 9.9, so in your equation x does not equal .9 like you said.

the short answer is no it does not equal 1

## Want to Vote on this Content?! No WSO Credits ?

Wtf is this shit...

## Want to Vote on this Content?! No WSO Credits ?

....

## Want to Vote on this Content?! No WSO Credits ?

...

## Want to Vote on this Content?! No WSO Credits ?

You just saw this on reddit didn't you

## Want to Vote on this Content?! No WSO Credits ?

Yes - my simplest 'explain in english' is that .3 repeating is generally known to equal one third, and 3 times one third equals 1

## Want to Vote on this Content?! No WSO Credits ?

That's a good way to explain it. Also if

1/3 = .3 repeating

2/3= .6 repeating

Add them together and you get

3/3=.9 repeating

1=.9 repeating

## Want to Vote on this Content?! No WSO Credits ?

Give it to this guy.

## Want to Vote on this Content?! No WSO Credits ?

Let me also do it with math:

0.999 repeating equals x.

10

x equals 9.999 repeating equals 9 + xx = 9Subtract x from both sides

9

therefore x=1

## Want to Vote on this Content?! No WSO Credits ?

Assuming you mean 10* .999 repeating = 9.999 repeating, this step is only true if the series converges (i.e it equals 1). In order to finish your proof you essentially assumed that what you were proving was true.

Are you retarded?

## Want to Vote on this Content?! No WSO Credits ?

All I'm doing is using that fact that the 9s go on infinitely. If they go on forever, then multiplying everything by 10 doesn't reduce the amount of 9s after the decimal point....they still go on forever (not forever - 1, because that value still equals 'forever')

## Want to Vote on this Content?! No WSO Credits ?

JDimon is right. This is a legitimate proof. He's not assuming anything about the series convergence- all he assumes is the presence of infinite 9s (follows by the assumption of repeated 9s). Multiplication by 10 is a well defined operation- even for infinite decimal places- as a "place shifter".

## Want to Vote on this Content?! No WSO Credits ?

Oh Cola Coca got the answer first. Everyone who's disagreeing with him isn't taking the time to think about what it means for the decimal to be repeating indefinitely

## Want to Vote on this Content?! No WSO Credits ?

Here's my answer:

Yes. When you want a repeated decimal, you just take that number and divided it by 9.

0.7777.....=7/9

0.5555.....=5/9

Thus, 0.999999.....should theoretically equal 9/9, and 9/9 = 1.

Do I get the SB?

## Want to Vote on this Content?! No WSO Credits ?

Gave it to Dimon, wasnt thinking of it that way but it makes sense.

You can prove this another way using negation

## Want to Vote on this Content?! No WSO Credits ?

how can one number equal another number? even if a limit, it still doesn't technically equal it...

plz splain

## Want to Vote on this Content?! No WSO Credits ?

This was how I thought of it:

If a <> b,

x exists where a < x < b or a > x > b.

If not, a=b

## Want to Vote on this Content?! No WSO Credits ?

The answer is yes. There is a long mathematical proof that you learn in calc 2.

But the easy straightforward answer is...

1/3 = .3 Repeated

2/3 = .6 Repeated

Add the two previous

3/3 = .9 Repeated

## Want to Vote on this Content?! No WSO Credits ?

Wikipedia has a pretty cool proof with (Dedekind) cuts too! I didn't know that one since my analysis class skipped the construction of real numbers, but it was nice. I liked it!

## Want to Vote on this Content?! No WSO Credits ?

Assume that 9.999.../=10

Then you can list a number that is greater than 9.999... and less than 10.

Since you can't, 9.999...=10

## Want to Vote on this Content?! No WSO Credits ?

1/3 + 1/3 + 1/3 = 3/3 = 1 and 1/3 is 0.33... so 0.3333..... + 0.3333..... + 0.3333.... = 0.9999 = 1

## Want to Vote on this Content?! No WSO Credits ?

Weird corollary imo: every terminating number has 2 equivalent decimal representations

## Want to Vote on this Content?! No WSO Credits ?

One terminating and one non-terminating?

## Want to Vote on this Content?! No WSO Credits ?

Models and bottles!

Did I get it right?

## Want to Vote on this Content?! No WSO Credits ?

I know why our financial system failed.

Because there are too many guys who think 0.9 is 1.

## Want to Vote on this Content?! No WSO Credits ?

There are several ways of showing this. An alternate version is using infinite series.

Let S(i) = i_Sum_k=1 .9*10^(-k)

And so .99 repeated is just Lim_(i--> infiniti) S(i)

But S(i) = .9* (1-10^(-i-1))/(1-1/10)

So Lim_(i--> infiniti) = .9*(1/(1-1/10)) = 1

-MBP

## Want to Vote on this Content?! No WSO Credits ?

Numbers are concepts. If the number isn't the same number, then it's not the same number. The idea of .9 repeating is that its as close as possible to 1 without actually being 1. Otherwise it would be 1. So I'm gonna ruin all the fun and say it's not possible based on the idea of what numbers are.

I hate victims who respect their executioners

## Want to Vote on this Content?! No WSO Credits ?

No it's a fact that .9 repeating is another representation of 1. There are many proofs for it. It's not counterintuitive if you look at how the real numbers are constructed.

-MBP

## Want to Vote on this Content?! No WSO Credits ?

MBP has it right. Any number has an infinite number of representations: for example, 1/2 can be written as 2/4, 3/6, etc..

.9 repeating is simply another representation of 1.

## Want to Vote on this Content?! No WSO Credits ?

## Want to Vote on this Content?! No WSO Credits ?

## Want to Vote on this Content?! No WSO Credits ?

## Want to Vote on this Content?! No WSO Credits ?

Must Reads on Wall Street OasisRelated Content on Wall Street Oasis