# Math: .9 repeating equals 1

Discussion in 'Community Discussion' started by Fearless Leader, Aug 23, 2007.

1. ### Fearless Leader macrumors 68020

Joined:
Mar 21, 2006
Location:
Hoosiertown
#1
I got bored after a math test and was just messing around and realized something that makes sense and doesn't make sense at the same time.

1/3 = .3 repeating
2/3 = .6 repeating
following the trend
3/3 = .9 repeating
but
3/3 = 1/1 which is 1.

Where Did I go wrong? or did I?

also: psst Q Add a math section. It'll be great. You know you want one.

2. ### ham_man macrumors 68020

Joined:
Jan 21, 2005

Joined:
Mar 21, 2006
Location:
Hoosiertown
#3
ohh thanks thats cool. I didn't even think of googleing/wiking this.

Its strange, I proved it (if only I did this a couple hundred years ago, I could have been remembered or something) but it doesn't seem right, but it is.

4. ### steamboat26 macrumors 65816

Joined:
May 25, 2006
Location:
Arlington VA
#4

Thats a long Wikipedia entry for one number!

5. ### ChrisBrightwell macrumors 68020

Joined:
Apr 5, 2004
Location:
Huntsville, AL
#5
Basically, the "lightbulb" moment for me was when I realized that an infinitessimal value, on the real number system, is equal to zero.

That is:

0.000...[infinitely many zeroes]...0001 is, on the real number line, equal to zero.

So ...
1/3 = 0.333...

1/3 * 3
= 0.333... * 3
= 0.999...
= 1 - 0.000...001
= 1 - 0
= 1

I feel like I grossly over-simplified it, but I hope that makes sense.

6. ### Rodimus Prime macrumors G4

Joined:
Oct 9, 2006
#6
ah I used to think about stuff like this. Then I got into college and engineering work. That when I learned anything past 3-4 decimal is pretty worthless any how. That includes when I am using scientific notation. I will only go 3-4 points past the decimal in my work and my answer will be 2-3 past.
Reason I know it is worthless is it effects the answer so little that it does not matter. My though is I am with in one hundredth of the correct answer so it is close enough.

7. ### jdechko macrumors 68040

Joined:
Jul 1, 2004
#7
And a more local discussion used to be here. Boy that one was fun.

Also, I prefer my explanation from said thread that if someone offered to give me a \$1,000,000 and I really only got \$999,999.99, I wouldn't be to upset.

8. ### bemylover macrumors regular

Joined:
Jun 20, 2005
#8
yep, 0.999999... is exactly 1. If it was not exactly 1 then there would be some other number that would be greater than 0.99999... and less then 1 and as there is no such number these two are the same.

Nice observation

9. ### Jasonbot macrumors 68020

Joined:
Aug 15, 2006
Location:
The Rainbow Nation RSA
#9
There was this funny simplification of fractions thing I did in maths a few years ago that showed how .999... is equal to 1. I can't remember it though.

10. ### johnee macrumors 6502a

#10

9 is a pretty evil number. it's always been jealous of 1, and it's been trying to make itself known for a long time now.

For instance, this little trick:
1 x 9 = 9
2 x 9 = 18 (1+8=9)
3 x 9 = 27 (2+7=9)
.
.
.
457 x 9 = 4113 (4+1+1+3=9)

EVIL!!!!

11. ### swiftaw macrumors 603

Joined:
Jan 31, 2005
Location:
Omaha, NE, USA
#11
Probably something like this

x = 0.99999....

so 10x = 9.99999........

so 10x - x = 9.99999..... - 0.99999.... = 9

so 9x = 9

so x = 9/9 = 1

Actually this method works to convert any reoccurring decimal into a fraction, for example
x = 0.838383.......
100x = 83.838383.....
99x = 83
x = 83/99

12. ### Jasonbot macrumors 68020

Joined:
Aug 15, 2006
Location:
The Rainbow Nation RSA
#12
Aaah! The memories Thanks!
luckily in grade 11 my casio FX 82-ES does fractions for me these days.

13. ### gertruded macrumors 6502

Joined:
Jul 5, 2007
Location:
Northwestern Illinois
#13
In the days when we used slide rules to do all our calculations, we were limited to 3 significant places. In that practical context .999 definitely is not equal to 1.00. I still laugh when I see calculations done computers displayed to 5 or more significant figures for ordinary engineering calculations.

The slide rule was an extraordinary device. Mine was a Post log log duplex versilog, made of bamboo. I still have it and it still works without electricity.

Gertrude

14. ### tominated macrumors 68000

Joined:
Jul 7, 2006
Location:
Queensland, Australia
#14
wow. i think i just had a mini stroke.

well, not really