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math problem debate

(15 posts)
  • Started 6 years ago by jack7h3r1pp3r
  • Latest reply from BobJam
  • Topic Viewed 1088 times

jack7h3r1pp3r
jack7h3r1pp3r
Posts: 2815

so one of my friends asked me this today and am wondering if anyone knows the answer to it?

here it goes

ok so if 1/3 = .33333......

then would 1/3 * 3 = 1

or would it equal .99999999.......

i think that it equals 1 but i'm not really sure any more

Posted 6 years ago
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Scott
Scott
Posts: 5618

Take a stand, man !
Does 3/3 = 1 or not?


•><((((º>
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•...><((((º>

Posted 6 years ago
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jack7h3r1pp3r
jack7h3r1pp3r
Posts: 2815

i'm not really sure lol :E

Posted 6 years ago
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ScottW
ScottW
Posts: 6609

Jack, the notation 0.333... is a mathematical shortcut for writing in decimal a fraction that has an infinite number of decimal places. You read it as, "point 3, 3, 3 repeating forever". If you continue to work with fractions, it's quite clear that:

1/3 * 3 = 1

This is read as "one third times three equals one." It is not as obvious in decimal, but it's still true that:

.333... * 3.0 = 1.0

Reading, "point 3, 3, 3, repeating forever times three point zero equals one point zero". It's just hard to wrap your head around an infinitely repeating decimal.

EDIT: proof of this is left to the reader. Also, check your calculator because it knows the answer as well.

Posted 6 years ago
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jack7h3r1pp3r
jack7h3r1pp3r
Posts: 2815

ok thats exactly what i thought i will show this to my friend lol

Posted 6 years ago
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Lighthouse
Lighthouse
Posts: 13598

Hey ScottW! What's with this "repeating forever"? I thought the word was "recurring"? :)

Posted 6 years ago
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whs
whs
Posts: 17584

I can't believe this - is this for real?

Posted 6 years ago
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Lighthouse
Lighthouse
Posts: 13598

One third's reality, two thirds don't know :)

Posted 6 years ago
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raphoenix
raphoenix
Posts: 14920

POST DELETED by raphoenix 09/12/2008

Posted 6 years ago
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ScottW
ScottW
Posts: 6609

Lighthouse, repeating, recurring. I guess we will have to agree to be separated by a common language. :)

Jack, while looking up "repeating decimal" at wikipedia, I saw that they have a special discussion on 0.999... including a proof that it's equal to 1. Check this math out folks:
http://en.wikipedia.org/wiki/R.....0.99999...

Posted 6 years ago
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jack7h3r1pp3r
jack7h3r1pp3r
Posts: 2815

my brain hurts too much to think about this math at the moment i've been doing homework since i woke up this morning lol so like 6-8 hrs blah

Posted 6 years ago
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Budohorseman
Budohorseman
Posts: 847

.3333333333333333333333333333...... is the approximate value of 1/3, as 1/3 is an irrational number (like pi or 2^.5).

Posted 6 years ago
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Lighthouse
Lighthouse
Posts: 13598

@ScottW. Thanks, I figured it might have been an American versus English thing, but wasn't sure.

Posted 6 years ago
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ScottW
ScottW
Posts: 6609

People can be irrational, life can be irrational, now you are telling me that numbers can be irrational? Is there no sanity in the world?!? :-)

Pi and the square root of 2 (2 ^ .5) are irrational numbers because they cannot be represented by the fraction of two integers. The fraction 1/3 is certainly a rational number, as is .333... because it can be represented as a rational. From Wikipedia: "The decimal expansion of an irrational number never repeats....":
http://en.wikipedia.org/wiki/I.....expansions

"Math class is tough. Let's go shopping!" -- Barbie Doll

Posted 6 years ago
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BobJam
BobJam
Posts: 1052

"I guess we will have to agree to be separated by a common language." Paraphrasing Winston Churchill, you are ScottW (and that is in Joda-speak).

Posted 5 years ago
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