So, where's the error... |
nfeese |
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Math 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 |
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Math Posts: 281 Location: Henry Clay | .9 repeating does equal 1 | ||
bperry |
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Math Posts: 281 Location: Henry Clay | 1/3 = .3 repeating 1=3(1/3) = 3(.3 repeating) = .9 repeating | ||
rmcquerr |
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Math Posts: 79 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 |
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Math Posts: 281 Location: Henry Clay | Thought this was funny: (series.jpg) Attachments ---------------- series.jpg (20KB - 332 downloads) | ||