find the unit digit of 2015^2016- 2016^2015?
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In Quantitative aptitude questions ask to find the last digit and last two digits of a power or large expressions. In this article explained different types of tools to serve as shortcuts to finding the last digits of an expanded power.
Find last digit of a number with power
First identify the pattern last digit (unit place) for power of numbers “N”
Digit N1 N2 N3 N4 N5 N6 N7 N8 N9
1 1 1 1 1 1 1 1 1
2 4 8 6 2 4 8 6 2
3 9 7 1 3 9 7 1 3
4 6 4 6 4 6 4 6 4
5 5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6 6
7 9 3 1 7 9 3 1 7
8 4 2 6 8 4 2 6 8
9 1 9 1 9 1 9 1 9
From the above table we can observe as follow
The last digit of power of 1, 5 & 6 is always comes same number as a unit place.
The last digit of power of 2 repeat in a cycle of numbers – 4, 8, 6 & 2
The last digit of power of 3 repeat in a cycle of numbers – 9, 7, 1 & 3
The last digit of power of 4 repeat in a cycle of numbers – 6 & 4
The last digit of power of 7 repeat in a cycle of numbers – 9, 3, 1, & 7
The last digit of power of 8 repeat in a cycle of numbers – 4, 2, 6 & 8
The last digit of power of 9 repeat in a cycle of numbers – 1 & 9
Explanation:
If Last digit ( Unit place ) of numbers having 1 , 5 & 6
( – – – – 1)n = ( – – – – 1)
(- – – – -5) n = ( – – – – 5)
(- – – – -6) n = (- – – – -6)
If the unit place ( Last digit ) of any number “ An ” having 2, 3, 7 or 8, then the unit place of that number depends upon the value of power “ n”
This is the process
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Find last digit of a number with power
First identify the pattern last digit (unit place) for power of numbers “N”
Digit N1 N2 N3 N4 N5 N6 N7 N8 N9
1 1 1 1 1 1 1 1 1
2 4 8 6 2 4 8 6 2
3 9 7 1 3 9 7 1 3
4 6 4 6 4 6 4 6 4
5 5 5 5 5 5 5 5 5
6 6 6 6 6 6 6 6 6
7 9 3 1 7 9 3 1 7
8 4 2 6 8 4 2 6 8
9 1 9 1 9 1 9 1 9
From the above table we can observe as follow
The last digit of power of 1, 5 & 6 is always comes same number as a unit place.
The last digit of power of 2 repeat in a cycle of numbers – 4, 8, 6 & 2
The last digit of power of 3 repeat in a cycle of numbers – 9, 7, 1 & 3
The last digit of power of 4 repeat in a cycle of numbers – 6 & 4
The last digit of power of 7 repeat in a cycle of numbers – 9, 3, 1, & 7
The last digit of power of 8 repeat in a cycle of numbers – 4, 2, 6 & 8
The last digit of power of 9 repeat in a cycle of numbers – 1 & 9
Explanation:
If Last digit ( Unit place ) of numbers having 1 , 5 & 6
( – – – – 1)n = ( – – – – 1)
(- – – – -5) n = ( – – – – 5)
(- – – – -6) n = (- – – – -6)
If the unit place ( Last digit ) of any number “ An ” having 2, 3, 7 or 8, then the unit place of that number depends upon the value of power “ n”
This is the process
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Mark me the brainliest
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Answer:
9
Explanation:
- we have 2015^2016- 2016^2015, let us take the first term of the expression 2015^2016.
- The unit digit of the term is 5. As we can observe, 5^1 = 5, 5^2 = 25, 5^3 = 125 and so on. Thus, in all powers of 5, the unit digit will always be 5.
- Now, we take the second term, 2016^2015. Here we can see the unit digit is 6. 6^1 = 6, 6^2 = 36, 6^3 = 216. Here, also we see that the unit digit will always be 6.
- Now we known that the unit digit of 1st term is 5 and 2nd term is 6. When we subtract the two, 5-6, the unit digit will become 9 and 5<6. Hence, the unit digit is 9.
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