Homework Help

1 = 0.999? How can you prove that 1 = 0.999999999999999999....?

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soccerfreak9 | Student, Grade 9 | (Level 2) eNoter

Posted October 27, 2011 at 11:09 PM via web

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1 = 0.999?

How can you prove that 1 = 0.999999999999999999....?

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litteacher8 | Middle School Teacher | (Level 1) Distinguished Educator

Posted October 27, 2011 at 11:39 PM (Answer #2)

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1 is .99 rounded.  The more nines you get, the closer to one you will be.  However, 1 will never exactly each 0.99999999, no matter how many nines you add.  You will get closer and closer until the differnece is so minimal that you decide to call it 1.

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soccerfreak9 | Student, Grade 9 | (Level 2) eNoter

Posted October 27, 2011 at 11:49 PM (Answer #3)

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Well... but can you also see it this way?

0.9999... = 1


x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999... (becuase x = 0.9999...)
9x = 9
x=1

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maadhav19 | College Teacher | (Level 2) Assistant Educator

Posted October 28, 2011 at 12:40 AM (Answer #4)

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Try this:

0.9999... /= 1

x=0.9999...

10x = 9.9999...

10x-x=9.0...

10x = 9+x = 9.999...

From your line:

10x - x = 9.9999... - 0.9999...

the next line  9x=9 does not follow. It should be

10x = 9.999....

 

 

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted November 2, 2011 at 10:45 AM (Answer #5)

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(1) You might also consider that 1/3+1/3+1/3=1 or .333333...+.33333...+.33333...=1.

Note that we are saying that .99999...=1 exactly, not approximately.

You will encounter other proofs using other ideas as you go through school: the sum of an infinite series, the limit of an infinite sequence, etc...

If you disagree that .99999999....=1, you have some company in the math world, though not much. Look up infinitesimals and you will find a fascinating history of a school of thought that differs from mainstream mathematics.

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wanasyraf | Student, Grade 9 | (Level 3) eNoter

Posted November 19, 2011 at 3:26 PM (Answer #6)

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It look like a infinite decimal

so

999999999999999.../1000000000000000...

as

S Infinity=a/1-r

 

 

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