To convert the decimal number 40 to base 5, we can divide the number by 5 and keep track of the remainders. Here’s how the conversion works step-by-step:
- Divide 40 by 5, which gives a quotient of 8 and a remainder of 0.
- Divide the quotient (8) by 5, which gives a quotient of 1 and a remainder of 3.
- Divide the new quotient (1) by 5, which gives a quotient of 0 and a remainder of 1.
Now, we collect the remainders from the divisions in reverse order:
- The first remainder is 1
- The second remainder is 3
- The third remainder is 0
Thus, the base 5 representation of the decimal number 40 is read from the last remainder to the first:
40 in base 5 is 130.