Predict the ones digit for the standard form of a number.how do you do it like 7 to the 100

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revolution's profile pic

revolution | College Teacher | (Level 1) Valedictorian

Posted on

7^1= 7

7^2= 49

7^3= 343

7^4=2401

7^5=16807

As you can see, the ones digit has a pattern 7,9,3,1,7.

As the 100th power is divisible by 4 (100/4=25), and the ones digit for 7^4 is 1, so similarly, the 100th power of 7, the ones digit would also be 1

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

1^100 = 1.Trevially the digit in unit place is 1

2^100= (2^4)^25 = (26)^26 digit in ones place is  like  that in6^25 in ones digit=6 in units or ones place.

3^100 = (3^4)25=(81)^25 = ends in ones place like 1^25 = 1, has 1 in its unit place

4^100=(4^2)50= 16^50= ends inunit place like 6^50 . Ending in 6 in ones place .

5^100 : Any positive integral power obviously inthis number has 5 in its ones digit.

6^100: has obviously 6 in its ones digit.

7^100= (7^4)^25=(2401)^25 behaves like 1^25 for its ones digit.Therefore has 1 in its ones digit.

8^10=(8^4)^25=(4096)^6. This number shall have its ones digit as in 6^25, which has 6 in units place.

9^100=(81)^50. This number has ones digit like 1^25. Therefore it has 1   in unit digit

10^100, has  obviously has 0 in ones digit.

Therefore, 1^100, 3^100,7^100 and 9^100 - These odd numbers or any odd number like this in units place to the power of 100 have 1 in  ones digit.

2^100, 4^100, 6^100 qnd 8^100 ---These even numers or any even number like this in unit place  to the power of 100 has 6 in ones digit.

10^100-This even number or any even number with zero in ones digit to the power of 100 has 0 in its ones place.

5^100; This number or any integer with 5 in its ones place to the power of 100 has 5 in  ones digit.

Hope this helps.

 

 

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