Investigation Seminar

1
Investigation Seminar

• ENDINGS
• Presented by Davina Cox and Georgie Vivers

2
Introduction

• There are two ways to find the answer when
  working with base numbers using to the power of.
• 73 or 7 x 7 x 7 which both equal 343
• This investigation will be using the single end
  digit in the answer (which in this case is 3).

3
If the base number is odd will the single end
digit be an odd number?

• 72 49
• 73 343
• 74 2401
• 75 16807

• 76 117649
• 77 823543
• 78 5764801
• 79 40353607
• If the base is an odd number then the single end
  digit of the answer is also an odd number.

4
If the base number is even will the single end
digit be an even number?

• 42 16
• 43 64
• 44 256
• 45 1024
• If the base is an even number then the single end
  digit is even

• 46 4096
• 47 16384
• 48 65536
• 49 262144
• When the base number is 4 the single end digit is
  either a 4 or 6.

5
Compare the sequences of end digits for different
odd bases.

• 32 9
• 33 27
• 34 81
• 35 243
• 36 729
• 37 2187
• 38 6561
• 39 19683

• 92 81
• 93 729
• 94 6561
• 95 59049
• 96 531441
• 97 4782969
• 98 43046721
• 99 3.87420489

6
Compare the sequences of end digits for different
even bases.

• 22 4
• 23 8
• 24 16
• 25 32
• 26 64
• 27 128
• 28 256
• 29 512

• 82 64
• 83 512
• 84 4096
• 85 32768
• 86 262144
• 87 2097152
• 88 16777216
• 89 1.34217728

7
The base number 5 always ends in 5 as the single
end digit.

• 52 25
• 53 125
• 54 625
• 55 3125
• 56 15625
• 57 78125
• 58 390625
• 59 1953125

8
The base number 6 always ends in 6 as the single
end digit.

• 62 36
• 63 216
• 64 1296
• 65 7776
• 66 46656
• 67 279936
• 68 1679616
• 69 10077696

9
Do any powers produce single end digits equal to
the base?

• 25 32
• 29 512
• 35 243
• 39 19683
• 45 1024
• 49 262144
• 55 1325
• 59 1953125

• 65 7776
• 69 10077696
• 75 16807
• 79 40353607
• 85 32768
• 89 1.34217728
• 95 59049
• 99 3.87420489

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In Conclusion

• This investigation we found all odd bases end in
  an odd single digit.
• All even bases ended in an even single digit.
• A pattern emerged with odd base numbers, ending
  with either 1,3,7,9, with the exception of base
  number 5.
• Base number 5 ended with the single end digit
  being 5.
• Base number 6 ended with the single end digit
  being 6.
• The powers of 5 9 produced single end digits
  equal to the base.

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The End