Maths and Numeracy

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Maths and Numeracy Investigation 39 Repeats
By Rachael Lawson Kyle Myers
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Repeats

• Unit fractions have a numerator of 1. Investigate
  those unit fractions whose decimal equivalents
  recur.

E.g.
0.333
0.1428571428571
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Can you predict whether the decimal expansion
for a particular unit fraction will be
terminating or recurring?

• What do you notice about the factors of the
  denominators of terminating decimals.

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Try converting these fractions to decimals
0.03030303.
0.3333..
0.2
0.014925373134328358
0.01123595505617977
0.1
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Prime Numbers

• Are numbers that only have two factors
  themselves and one.

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0.06666..

0.04166666
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5
12
3
0.25
0.04
4
3
2
2
5
5
2
2
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For the decimal expansion of the fraction to
terminate the only prime factors of the
denominator have to be either 2 and or 5.
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Question?? How many digits will there be in the
recurring cycle for a particular unit fraction.
Answer. Complex area of mathematics known as the
number theory.
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Which unit fractions have an even number of
digits in their recurring cycle?
Prime number
Prime number
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Summary

• Factors of denominator have to be 2 and or 5 in
  order to terminate.

• For an even number of digits in the
  recurring cycle the denominator has to be a prime
  number.