Unit Digit:- The last digit of a number is called unit digit.
⬤ The unit digit of resultant value depends upon the unit digits of all participating numbers.
Ex:- Find the unit digit of 96 + 82 + 73 + 26 + 42
Sol:- No need to calculate the sum. Just add unit digits of all numbers and take only unit digit of resultant at every step & ignore all other digits.
Ex:- Find the unit digit of 96×82×73×26×42
Sol:-
Ex:- Find the unit digit of 198 × 4312 × 17 × 239 × 892
Sol:-
(xyz)ⁿ
z is the last digit (unit digit) of base.
To find out the last digit in (…….xyz)ⁿ, following steps to be followed:-
Divide the index ‘n’ by 4, then
Case(i): If remainder is Zero
then check if z is odd (except 5), the unit digit = 1 and if z is even, then unit digit = 6
Case(ii):
If remainder is 1 then unit digit = unit digit of (z)
If remainder is 2 then unit digit = unit digit of (z)²
If remainder is 3 then unit digit = unit digit of (z)³
Note: If z is 5 then unit digit is always 5.
Ex:- Find the unit digit of (9783)⁵⁹⁶
Sol:- \(\frac{{596}}{4}\)⟶R = 0 7 z i.e. 3 is odd ⟹ unit digit = 1 Answer
Note: If z is 6 then unit digit is always 6
Ex:- Find the unit digit of (97868)⁵⁹⁶.
Sol:- \(\frac{{596}}{4}\) ⟶R = 0 & z i.e. 8 is even ⟹ unit digit = 6 Answer
Ex:- Find the unit digt of (9783)⁵⁹⁷, (9782)⁵⁹⁸, (9787)⁵⁹⁹
Sol:-
Ex:- Find the unit digit of (289175)³²¹⁶⁵⁹³
Sol:- Since z = 5, So no matter what power is, unit digit will always be 5 Answer
Ex:- Find the unit digit of (345986)⁸⁷⁹⁵²
Sol:- Since z = 6, So no matter what power is, unit digit will always be 6 Answer
Last Two Digit of a Number:-
Case(i):- When n is ending in 1, 3, 7, 9 i.e. odd except 5
● Higher power of 3, 7, 9 can be converted into a number ending in 1 then this property can be applied for numbers ending in 3, 7, 9 as well.
Ex:- Find the last two digits of (8779367)⁶⁸⁷.
Sol:-