How do you predict the ones digit for the standard form of the number 7 to the 100 power?it's exponents

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cburr's profile pic

cburr | Middle School Teacher | (Level 2) Associate Educator

Posted on

Look at the first several numbers in this series:

7^1 = 7

7^2 = 49

7^3 = 343

7^4 = 2401

7^5 = 16807

7^6 = 117649

7^7 = 823543

7^8 = 5764801

7^9 = 40353607

As you can see, there is a pattern in the ones digit.  It goes:

7, 9, 3, 1, 7, etc.

So, the ones digit in the 4th, 8th, 12th, etc numbers will be 1.  Since 100 is divisible by 4, the 100th number in the series will also have 1 in the ones digit.

 

revolution's profile pic

revolution | College Teacher | (Level 1) Valedictorian

Posted on

There is a pattern to this powers, if you use the base to the power of the index.

Like this:

  1. 7^1=7
  2. 7^2=49
  3. 7^3=343
  4. 7^4=2401
  5. 7^5= 16807

As you can see, there is a pattern of 7,9,3,1 in the ones digit as it progress to the 100th power. For the power of 4, the ones digit is simply one. And as what cburr said above, 100 can also be divided by the number 4 (100/4=25)

So, we can say the last digit (ones) for the 100th power would be 1

 

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