Question

Write the unit digits for the cube of 109.
A. 1
B. 7
C. 9
D. 3

Answer 1

Hint: In this problem we need to multiply 109 thrice to get the digit of the one’s place. One’s place means the first place from the right of the number and second from the right is called the tenth place and so on. Doing this will solve your problem and will give you the right answer.

Complete step-by-step solution:
Here we need to do the cube of 109. We know that the cube of any number ‘a’ is $a \times a \times a $ and is denoted by ${{\text{a}}^3}$.
And unit digit or one place in any of the numbers is the first number form the right of the number.
So, we need to find a cube of 109.
So, we do $109 \times 109 \times 109 = 1295029.$
We can clearly see that at the rightmost number in 1295029 is 9.
So, again we have to take the cube of 9 and that is $9 \times 9 \times 9 = 729.$
At the unit place, there is 9.
As we can see on taking the cube of a number which has a unit digit as 9 then we always get 9 as the unit digit in the cube of that particular number.
So, the right answer is 9.
Hence the correct option is C.

Note: When you get to solve such problems you need to proceed as above we have done. The cube of the number is the result of multiplying a whole number by itself twice. Example: $3 \times 3 \times 3 = 27.$, so 27 is a cube number. The whole number is used three times, just like the sides of a cube. Each digit is different place value. And the rightmost digit is the digit at one’s place. Knowing this will help you to solve your problems further.