Mathematics Instructional Learning Community
Mathematics Instructional Learning Community
The Mathematics Instructional Learning Community (MILC) Project is an alliance among Fayette County Public Schools (FCPS) math teachers focusing on:
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"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity." (Howard W. Eves)
So, where's the error...
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nfeese
Posted 10/24/2005 12:21 PM (#221)
Subject: So, where's the error...
Math

500100100252525
Location: IAKSS		MathCounts Puzzle of the Week:

If x=.9 repeating, then 10x = 9.9 repeating.
So, 10x - x = 9.9 repeating -.9 repeating.

If that is true, then, 9x/9 = 9/9 so, x must = 1 and therefore .9 repeating actually equals 1.

We know that is not true and therefore the problem is incorrect.

So, where's the error?
bperry
Posted 10/24/2005 4:26 PM (#225 - in reply to #221)
Subject: RE: So, where's the error...


Math

Posts: 281
100100252525
Location: Henry Clay		.9 repeating does equal 1
bperry
Posted 10/24/2005 4:27 PM (#226 - in reply to #221)
Subject: RE: So, where's the error...


Math

Posts: 281
100100252525
Location: Henry Clay		1/3 = .3 repeating

1=3(1/3) = 3(.3 repeating) = .9 repeating
rmcquerr
Posted 10/24/2005 9:09 PM (#228 - in reply to #221)
Subject: RE: So, where's the error...
Math

Posts: 79
252525
Location: Tates Creek		.9 repeating is actually one of the only few ambiguous cases in mathematics. Its in an error in the notation we have accepted for decimal expansions. Another proof that .9 repeating equals one is through geometric series. 9\10 + 9\100 + 9\1000 + ...
So a = 9\10 and r = 1\10, thus a/(1-r) = 1.
bperry
Posted 12/17/2005 11:59 PM (#468 - in reply to #221)
Subject: RE: So, where's the error...


Math

Posts: 281
100100252525
Location: Henry Clay		Thought this was funny:



(series.jpg)



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