Final answer:
To convert a number from base 10 to another base using subtraction or division-remainder, divide the original number by the target base and record the remainders in reverse order. Repeat this process until the quotient becomes 0. Example conversions include 45810 to base 2, 67710 to base 8, 151810 to base 16, and 440110 to base 5.
Step-by-step explanation:
To convert from base 10 to another base using subtraction or division-remainder, we repeatedly divide the original number by the target base and keep track of the remainders. The final answer is the series of remainders in reverse order.
a) To convert 458 from base 10 to base 2, we divide 458 by 2. The remainder is 0. Then we divide the quotient (229) by 2 again, getting a remainder of 1. We continue this process until the quotient becomes 0. The remainders in reverse order are 111001010.
b) To convert 677 from base 10 to base 8, we divide 677 by 8. The remainder is 5. Then we divide the quotient (84) by 8 again, getting a remainder of 4. We continue this process until the quotient becomes 0. The remainders in reverse order are 1245.
c) To convert 1518 from base 10 to base 16, we divide 1518 by 16. The remainder is 14, which represents E in base 16. Then we divide the quotient (94) by 16 again, getting a remainder of 14. We continue this process until the quotient becomes 0. The remainders in reverse order are 5EE.
d) To convert 4401 from base 10 to base 5, we divide 4401 by 5. The remainder is 1. Then we divide the quotient (880) by 5 again, getting a remainder of 0. We continue this process until the quotient becomes 0. The remainders in reverse order are 10001.