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Aluaeia
RealPoor Master of Posts
Joined: 06 Jun 2003
Posts: 5670
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 Posted: 10/18/05 - 12:10 Post subject: Stupid Math Question
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I forgot my high school math, anyone remember how to convert nonterminating repeating decimals into a fraction?
In particular, 0.72222222222...
I'm playing with cellular automata and the lambda threshold for a single dot seed in the system I'm using seems to be at that number, so I'm trying to figure out the math behind it.
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Owyyn
RealPoor Guru
Joined: 11 Oct 2002
Posts: 2900
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Devook
RealPoor Guru
Joined: 31 Mar 2004
Posts: 2373
Location: Ypsilanti or Troy, MI
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Posted: 10/18/05 - 13:44 Post subject:
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Well... to create a repeating fraction of a particular number, you take that number over 99.
Like x/99 is .xxxxxxxxx~
.72222222 is .7 + .02222222222 so it is 7/10 + 2/99 * .1 which goes to 7/10 + 2/990. Figure that out, and simplify.
There's probably an easier way to do that, but that's just what can figure out from looking at it.
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Smin
Luke Warm
Joined: 11 Oct 2002
Posts: 163
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Posted: 10/18/05 - 18:00 Post subject:
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Non-repeating decimals
These are also called terminating decimals because they don't go on forever.
Example 1: Convert 0.45 to a fraction.
Step 1: Let x = 0.45.
Step 2: Count how many numbers there are after the decimal point. In this case, there are 2.
Step 3: Multiply both sides by 100, because 100 has 2 zeroes. We get 100x = 45.
Step 4: Solve for x. In this case x = 45/100. Using Euler's Formula to reduce the fraction, we get x = 9/20.
Simple repeating decimals
You can tell if it is a simple repeating decimal number if the repeating part starts with the first number after the decimal point.
Example 2: Convert 4.372372372... to a fraction.
Step 1: Let x = 4.372372. Call this equation #1.
Step 2: Count how many numbers there are in the repeating part. In this example, the repeating part is 372. So there are 3 numbers in the repeating part.
Step 3: Multiply both sides by 1000, because 1000 has 3 zeroes. We get 1000x = 4372.372372... Call this equation #2.
Step 4: Subtract equation #1 from equation #2:
1000x=4372.372372
x= 4.372372
999x=4368.0
Solving for x, we get x = 4368/999. Using Euler's Formula to reduce the fraction, we get x = 1456/333.
Ugly repeating decimals
Example 3: Convert 2.173333... to a fraction.
Step 1: Let x = 2.173333. Call this equation #1.
Step 2: Count how many non-repeating numbers there are after the decimal point. In this case, there are 2.
Step 3: Multiply both sides by 100, because 100 has 2 zeroes. We get 100x = 217.3333... Call this equation #2.
Step 4: Now that we have equation #2 as a simple repeating decimal number, we can carry out the same strategy as in Example 2, starting with step 2:
1000x=2173.333
100x= 217.333
900x=1956.0
Solving for x, we get x = 1956/900.
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Aluaeia
RealPoor Master of Posts
Joined: 06 Jun 2003
Posts: 5670
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Posted: 10/18/05 - 20:27 Post subject:
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Awesome!
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