How to find the unit digit of large powers numbers?
Answers
Answered by
1
Divide the power by '4'
If the remainder is '1', just raise the unit digit to power 1.
Eg: (abc)^1233. 1233/4 = Remainder 1
Hence unit digit = c^1
Similarly for remainders 2 and 3, just find out (unit digit of the question)^respective remainder.
If remainder = 0,
if unit digit of question is odd(except 5), then the answer will be 1
If unit digit is even, then the answer will be 6.
N.B:1^any power = 1(unit's place)
5^any power = 5(unit's place)
6^any power = 6(unit's place)
If the remainder is '1', just raise the unit digit to power 1.
Eg: (abc)^1233. 1233/4 = Remainder 1
Hence unit digit = c^1
Similarly for remainders 2 and 3, just find out (unit digit of the question)^respective remainder.
If remainder = 0,
if unit digit of question is odd(except 5), then the answer will be 1
If unit digit is even, then the answer will be 6.
N.B:1^any power = 1(unit's place)
5^any power = 5(unit's place)
6^any power = 6(unit's place)
Answered by
0
Remember the following tricks and tips -
1. If the unit digit is 1, even if you raise it to any power, it'll still remain 1. The same thing applies for digits 0, 5, and 6, they give the same digit even when raised to some power.
2. If the unit digit of some number is 9 and you raise it to some odd power, the unit digit will remain same (9), and when you raise it to some even power, the unit digit would be 1.
3. Numbers having even numbers as unit digits raised to any power would result in an even numbered unit digit. Odd numbers would result in odd.
4. For all digits, there is a fixed pattern of repetition, I'll explain through an example. Suppose the unit digit is 4, and the power to which the number is raised is x.
When x=1, unit digit = 4
When x=2, unit digit = 6
When x=3, unit digit = 4
When x=4, unit digit = 6
See the pattern? This pattern is followed by all digits, just the number of turns after repetition starts is different for each digit. The number of terms after which repetition begins is called that number's cyclicity.
These tips would come in handy hen solving problems related to finding unit digit of numbers.
1. If the unit digit is 1, even if you raise it to any power, it'll still remain 1. The same thing applies for digits 0, 5, and 6, they give the same digit even when raised to some power.
2. If the unit digit of some number is 9 and you raise it to some odd power, the unit digit will remain same (9), and when you raise it to some even power, the unit digit would be 1.
3. Numbers having even numbers as unit digits raised to any power would result in an even numbered unit digit. Odd numbers would result in odd.
4. For all digits, there is a fixed pattern of repetition, I'll explain through an example. Suppose the unit digit is 4, and the power to which the number is raised is x.
When x=1, unit digit = 4
When x=2, unit digit = 6
When x=3, unit digit = 4
When x=4, unit digit = 6
See the pattern? This pattern is followed by all digits, just the number of turns after repetition starts is different for each digit. The number of terms after which repetition begins is called that number's cyclicity.
These tips would come in handy hen solving problems related to finding unit digit of numbers.
Similar questions