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To find the units digit of 399 the question being asked is:
What is (399) MOD 10?
This does not necessitate evaluation of 399 before the modulus is done, as it can be done whenever it is possible during the multiplication as any multiple of 10 multiplied by 3 is still a multiple of 10.
The first few powers of 3 modulus 10 are:
31 MOD 10 = 3
32 MOD 10 = (3 x 31) MOD 10 = (3 x 3) MOD 10 = 9
33 MOD 10 = (3 x 32) MOD 10 = (3 x 9) MOD 10 = 27 MOD 10 = 7
34 MOD 10 = (3 x 33) MOD 10 = (3 x 7) MOD 10 = 81 MOD 10 = 1
35 MOD 10 = (3 x 34) MOD 10 = (3 x 1) MOD 10 = 3
36 MOD 10 = (3 x 35) MOD 10 = (3 x 3) MOD 10 = 9
At this point, it can be seen that the answer is a repeating pattern of 3, 9, 7, 1, 3, 9, ...
So we need the 99th element of this pattern.
The pattern is a repeat of 4 digits, so we calculate 99 MOD 4 = 3. So the 3rd element of the repeating part is the answer: 7.
(If the power MOD 4 had been 0, it would have been the 4th element of the pattern: 1)
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How do you find the unit digit of 3127 power 173?
The unit digit of 3127173 is the unit digit of 7173. The other digits of 3127 are multiples of 10 and so they cannot contribute to the unit digit. Now the unit digits of the powers of 7 are Power -- Unit digit 0 -- 1 1 -- 7 2 -- 9 3 -- 3 4 -- 1 and you are back into the loop (of 1-7-9-3). So, you only need consider 7 to the power 173 modulo 4. That is, the remainder when 173 is divided by 4. 173 = 1 mod 4 So the unit digit of 3127173 is the same as the unit digit of 7173 which is the unit digit of 71 which is 7.
What is the predecessor of 3 digit number?
A smaller 3 digit number or a 2 digit number (99).
What is the unit digit in the product of 684x759x413x676?
Any digit in the tens or higher place has no influence on the answer. So it is the unit digit of 4*9*3*6 = unit digit of 6*3*6 = unit digit of 8*6 = 8
What is the unit digit in the sum of first 99 whole numbers?
IN WHOLE NUMBER FIRST DIGIT IS 0 SO THAT WE HAVE TO SUM 1-98 NUMBERS :-SUM OF 1-10 IS 55 SO IN SUM OF EACH 11-20,21-30......THE UNIT DIGIT WILL COME 5 SO FOR THAT WE MULTIPLY 5*9+1+2+3+4+5+6+7+8 AFTER THIS CALCULATION WE GOT 1 AS A UNIT DIGIT NUMBER
If you add a two digit number to a two digit number do you get a four digit number?
No. When adding the smallest 2 digit number (= 10) to the smallest 2 digit number (again, 10) the result is a 2 digit number (10 + 10 = 20). When adding the largest 2 digit number (= 99) to the largest 2 digit number (again, 99) the result is a 3 digit number (99 + 99 = 198). As you can see, you'll either get a 2 or 3 digit number, but never a 4 digit number.
