Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register
 

Round 0.4999999 to integer?

This topic has 6 expert replies and 8 member replies
pinktoadette Just gettin' started! Default Avatar
Joined
20 Jun 2008
Posted:
15 messages
Target GMAT Score:
750
Round 0.4999999 to integer? Post Wed Feb 29, 2012 7:54 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Dumb question

    When you round 0.499999, is it 0 or 1? I thought 1 at first but,...
    ..if it's repeating 9s? It never reaches 0.5, so 0..?


    Thanks!!

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    krusta80 Really wants to Beat The GMAT!
    Joined
    14 Mar 2011
    Posted:
    143 messages
    Followed by:
    5 members
    Thanked:
    34 times
    Post Wed Feb 29, 2012 9:25 pm
    pinktoadette wrote:
    Dumb question

    When you round 0.499999, is it 0 or 1? I thought 1 at first but,...
    ..if it's repeating 9s? It never reaches 0.5, so 0..?


    Thanks!!
    0

    GMAT/MBA Expert

    Post Fri Mar 02, 2012 8:39 am
    0... .5 is the cutoff. Don't round multiple times.

    _________________
    If you find my posts helpful. Please take the time to click the "thank" icon at the top of the page and/or follow me!

    Full Length GMAT Exam | GMAT classes | GMAT Prep|GMAT Tutoring|MBA Admissions Consulting|Stratus Prep Reviews

    Post Sat Mar 03, 2012 1:31 pm
    pinktoadette wrote:
    When you round 0.499999, is it 0 or 1? I thought 1 at first but,...
    ..if it's repeating 9s? It never reaches 0.5, so 0..?
    Your question about the repeating 9's is interesting.

    It can be argued that 0.4999...(9's repeating forever) is equal to 0.5

    Proof #1
    If 0.4999...(forever) does not equal 0.5, then there must exist some number BETWEEN 0.4999... and 0.5
    Since no such number exists, we must conclude that 0.4999.... is equal to 0.5, in which case rounding it to the nearest integer would be 1.

    Proof #2
    Another way to look at it is to say that 0.4999..... = 0.4 + 0.0999...

    Well, 0.0999... is equal to 0.1
    Here's why.
    We know that 1/30 = 0.0333...
    So, 3/30 = 0.0999...
    But we already know that 3/30 = 0.1
    So, 0.0999... must equal 0.1, which means that 0.4999..... = 0.4 + 0.0999... = 0.4 + 0.1 = 0.5


    Having said all of that, this would never be tested on the GMAT.


    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    vikram4689 GMAT Titan
    Joined
    01 Nov 2009
    Posted:
    1324 messages
    Followed by:
    13 members
    Thanked:
    100 times
    Post Sat Mar 03, 2012 8:14 pm
    Brent,
    I think answer would be 0 because in explanation above we round off 2 times which we should not do.

    I tried this in EXCEL as well Smile
    0.4999 = 0.500 = 0.50 = 0.5 = 0 [no. of digits = no. of significant digits allowed, and then i reduced the no. of significant digits one by one]

    _________________
    Premise: If you like my post
    Conclusion : Press the Thanks Button Wink

    Post Sat Mar 03, 2012 11:59 pm
    vikram4689 wrote:
    Brent,
    I think answer would be 0 because in explanation above we round off 2 times which we should not do.

    I tried this in EXCEL as well Smile
    0.4999 = 0.500 = 0.50 = 0.5 = 0 [no. of digits = no. of significant digits allowed, and then i reduced the no. of significant digits one by one]
    Well, we're already getting into some esoteric/out-of-scope territory, but I will suggest that we're not rounding two times. First, we're recognizing that 0.4999... = 0.5 (no rounding yet), and then we round 0.5 to 1.

    Also, I'm having a hard time believing that you entered an infinite number of 9's in Excel. That would have taken quite a while Smile

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    krusta80 Really wants to Beat The GMAT!
    Joined
    14 Mar 2011
    Posted:
    143 messages
    Followed by:
    5 members
    Thanked:
    34 times
    Post Sun Mar 04, 2012 12:07 am
    Brent@GMATPrepNow wrote:
    vikram4689 wrote:
    Brent,
    I think answer would be 0 because in explanation above we round off 2 times which we should not do.

    I tried this in EXCEL as well Smile
    0.4999 = 0.500 = 0.50 = 0.5 = 0 [no. of digits = no. of significant digits allowed, and then i reduced the no. of significant digits one by one]
    Well, we're already getting into some esoteric/out-of-scope territory, but I will suggest that we're not rounding two times. First, we're recognizing that 0.4999... = 0.5 (no rounding yet), and then we round 0.5 to 1.

    Also, I'm having a hard time believing that you entered an infinite number of 9's in Excel. That would have taken quite a while Smile

    Cheers,
    Brent
    The interesting thing about infinite 9's as a decimal is that it has no equivalent fraction. Smile

    That said, I'm wondering why the original poster is asking the question? I've seen something like this happen in computer programming when dealing with decimals. In those cases, it's important to realize that the computer isn't rounding as much as it's simply misrepresenting the TRUE value, which in this case would be .5



    Last edited by krusta80 on Sun Mar 04, 2012 12:10 am; edited 1 time in total

    vikram4689 GMAT Titan
    Joined
    01 Nov 2009
    Posted:
    1324 messages
    Followed by:
    13 members
    Thanked:
    100 times
    Post Sun Mar 04, 2012 12:09 am
    Haha, but we are talking about 0.4999999 and not 0.4999999....infinity.
    and 0.4999999 is NOT equal to 0.5 so if we have to answer "0.4999999 to integer?" then it would be 0

    _________________
    Premise: If you like my post
    Conclusion : Press the Thanks Button Wink

    Post Sun Mar 04, 2012 12:11 am
    krusta80 wrote:
    The interesting thing about infinite 9's as a decimal is that it has no equivalent fraction. Smile
    I'm not sure I agree with that.

    We know that 1/9 = 0.1111...(with infinite 1's)
    And 2/9 = 0.2222...(with infinite 2's)
    And 3/9 = 0.3333...(with infinite 3's)
    ...
    9/9 = 0.9999...(with infinite 9's)

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    krusta80 Really wants to Beat The GMAT!
    Joined
    14 Mar 2011
    Posted:
    143 messages
    Followed by:
    5 members
    Thanked:
    34 times
    Post Sun Mar 04, 2012 12:12 am
    Brent@GMATPrepNow wrote:
    krusta80 wrote:
    The interesting thing about infinite 9's as a decimal is that it has no equivalent fraction. Smile
    I'm not sure I agree with that.

    We know that 1/9 = 0.1111...(with infinite 1's)
    And 2/9 = 0.2222...(with infinite 2's)
    And 3/9 = 0.3333...(with infinite 3's)
    ...
    9/9 = 0.9999...(with infinite 9's)

    Cheers,
    Brent
    But we know that 9/9 is 1. Smile

    Actually...looks like we're both right...unless of course Wiki is wrong. lol

    http://en.wikipedia.org/wiki/0.999...



    Last edited by krusta80 on Sun Mar 04, 2012 12:15 am; edited 1 time in total

    Post Sun Mar 04, 2012 12:12 am
    vikram4689 wrote:
    Haha, but we are talking about 0.4999999 and not 0.4999999....infinity.
    and 0.4999999 is NOT equal to 0.5 so if we have to answer "0.4999999 to integer?" then it would be 0
    Agreed, but I've been responding to the second part of the original question, that asks what happens if the 9's are repeating.

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    vikram4689 GMAT Titan
    Joined
    01 Nov 2009
    Posted:
    1324 messages
    Followed by:
    13 members
    Thanked:
    100 times
    Post Sun Mar 04, 2012 12:15 am
    this is what Brent was saying i.e. 0.999... = 1
    Quote:
    But we know that 9/9 is 1.
    I think we should not delve more as we all agree
    0.499999 to integer is 0
    0.4999... to integer is 1

    _________________
    Premise: If you like my post
    Conclusion : Press the Thanks Button Wink

    krusta80 Really wants to Beat The GMAT!
    Joined
    14 Mar 2011
    Posted:
    143 messages
    Followed by:
    5 members
    Thanked:
    34 times
    Post Sun Mar 04, 2012 12:17 am
    vikram4689 wrote:
    this is what Brent was saying i.e. 0.999... = 1
    Quote:
    But we know that 9/9 is 1.
    I think we should not delve more as we all agree
    0.499999 to integer is 0
    0.4999... to integer is 1
    Agreed.

    Post Sun Mar 04, 2012 12:23 am
    It looks like it's unanimous!

    Now I can go to bed.... Smile

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    rakesh4u119 Just gettin' started!
    Joined
    01 Apr 2012
    Posted:
    1 messages
    Post Mon Apr 02, 2012 4:18 am
    Try below Funda's..

    Pure Recurring to Fractions
    FUNDA 1: If a number is of the form of 0.ababab……. then divide the repeating digits with as many 9’s as we have repeated digits.
    eg. 0.363636… =36/99 =11/4

    Mixed Recurring to Fractions

    FUNDA 2: If N = 0.abcbcbc…. Then
    N =(abc - a)/990
    As many 9' s as repeated digits followed by as many zero as non repeated digits
    Re peated & non repeated digits Non repeated digits
    -
    -
    eg. 0.25757…..=(257 - 2)/990=255/990 =17/66

    FUNDA 3:If N = a.bcbc…. Then
    Write N = a + 0.bcbc….
    Proceed as Funda 1
    5.3636… = 5 + 0.3636… =5 + 36/99 = 11/59

    Best Conversation Starters

    1 vipulgoyal 32 topics
    2 hemant_rajput 23 topics
    3 guerrero 18 topics
    4 abhirup1711 17 topics
    5 sana.noor 16 topics
    See More Top Beat The GMAT Members...

    Most Active Experts

    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    211 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    137 posts
    3 image description Jim@StratusPrep

    Stratus Prep

    60 posts
    4 image description Jon@Admissionado

    Admissionado

    49 posts
    5 image description David@VeritasPrep

    Veritas Prep

    31 posts
    See More Top Beat The GMAT Experts