Question

What is the difference between 431five and 204five in base five?

a) 222five
b) 221five
c) 223five
d) 220five

Answer 1

To find the difference between 431five and 204five in base five, you perform subtraction using base five rules. After borrowing for the ones place and working your way through, the result is 222five.

Step-by-step explanation:

Finding the Difference in Base Five

To find the difference between 431five and 204five in base five, we subtract the two numbers just as we would in the decimal system, but using base five rules where each place can only hold the digits 0 through 4.

1. Starting from the right, we subtract the ones place: 1 - 4 cannot be done without borrowing; so, we borrow from the next column, where 3 becomes 2 and we add 5 to the 1, making it 6 in base five (which is actually 1 in decimal). 6 - 4 is 2 in base five.
2. Moving to the tens place, after borrowing we have 2 - 0 which is 2 in base five.
3. Finally, in the hundreds place, there's nothing to subtract from 2, so it remains 2 in base five.

Therefore, the difference between 431five and 204five in base five is 222five.