Repeats

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Repeats!

• By Nik and Al Pal

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So what is a Repeat?

• They are known as recurring numbers
• Repeats and recurring numbers occur when units
  fractions do not evenly divide into each other
• Unit Fractions are fractions that have a
  numerator of 1

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Terminating Decimals

• Unit fractions that do divide evenly are
  terminating decimals
• By terminating we mean that they stop.
• Numbers that Terminate, eg ½ 0.5 are called
  REGULAR NUMBERS

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Two types of recurring numbers

• IRRATIONAL DECIMALS are when recurring numbers
  continue infinitely without repeating,
• example 1/17 0.0588732529

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• REPEATING NUMBERS are when recurring numbers
  become periodic, meaning after a certain period
  of time, the cycle repeats
• example 1/90.111111
• This means they continue on and on
• and on
• and on..
• and on.

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Can you predict whether the decimal expansion
for recurring decimals will eventually terminate?
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Where we started

• We started with a simple hand held calculator
• Worked on Microsoft Excel spread-sheet

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E X C E L E X C E L

• Excel work sheet only allowed the decimals to go
  to 15 places
• We were able to make a formula using excel where
  the division was done for us
• Example A1/B1

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Manual Process

• Using pen, paper and our brains, we were able to
  see that these recurring numbers were never going
  to end, ever.

0.1666666
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1 4 4 4 4 4
1. 000000
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Unit Fractions made from the factors of nine
We discovered that when a 9 is added to the
denominator a zero adds to the decimal equivalent
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Conclusion
In summary we discovered that recurring numbers
never terminate and that the number nine is
pretty groovy.