median
don steward
mathematics teaching 10 ~ 16

Tuesday, 4 December 2007

repeating repeating repeating

the repeating pattern for sevenths is fairly easily remembered since it goes 14 28 57 which is double 7, then double 14, then double 28 ... oops!

the reasons for this aren't easy to fathom
  • 100 divided by 7 is 14 remainder 2
  • so the next block of two digits will be the result of dividing 200 by 7, which will be 28 (remainder 4)
  • so the next block of two digits will be the result of dividing 400 by 7, which will be 57 (not 56) remainder 1 - when the process repeats

what is sometimes seen as remarkable is that if you split this six digit (printing) block into two parts and add: 142 + 857 you get 999 and if you split it into three parts and add: 14 + 28 + 57 you get 99

this neat property is shared by the block of six repeating numbers for thirteenths and other decimal equivalents to fractions

and also...

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