# 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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### 2 Answers

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**

**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.