Convert the base-ten number to a numeral in the indicated base.

503 to base five

A) 3040five
B) 4030five
C) 3004five
D) 4003five

Convert 504 to base five

To convert the base-ten number 503 to base five, follow these steps:

Step 1: Divide the number by 5 and write down the remainder.
503 ÷ 5 = 100 remainder 3

Step 2: Divide the resulting quotient from step 1 by 5 and write down the remainder.
100 ÷ 5 = 20 remainder 0

Step 3: Repeat step 2 with the new quotient.
20 ÷ 5 = 4 remainder 0

Step 4: Divide the resulting quotient from step 3 by 5 and write down the remainder.
4 ÷ 5 = 0 remainder 4

Step 5: Write down the remainders obtained from each step in reverse order.
4040

Therefore, the numeral representation of 503 in base five is 4040five. None of the given options (A, B, C, D) matches the correct answer.

To convert the base-ten number 503 to base five, we need to divide the number repeatedly by 5 and record the remainders until we reach 0. Let's follow the steps:

1. Start by dividing 503 by 5: 503 ÷ 5 = 100 with a remainder of 3. Write down the remainder as the rightmost digit.

2. Divide the quotient from step 1 (100) by 5: 100 ÷ 5 = 20 with a remainder of 0. Write down the remainder.

3. Divide the new quotient (20) by 5: 20 ÷ 5 = 4 with a remainder of 0. Write down the remainder.

4. Divide the new quotient (4) by 5: 4 ÷ 5 = 0 with a remainder of 4. Write down the remainder.

5. Since the quotient is now 0, we stop the division process.

Now, let's look at the answer choices and find the one that matches the remainders we obtained:

A) 3040five: The remainders we obtained were 3, 0, 0, and 4. This matches the answer choice.

B) 4030five: This does not match the remainders obtained.

C) 3004five: This does not match the remainders obtained.

D) 4003five: This does not match the remainders obtained.

Therefore, the correct answer is A) 3040five.

503(base 10) =

4*125 + 0*25 + 0*5 + 3*1
=4*5^3 + 0*5^2 + 0*5^1 + 3*5^0
= 4003 (base 5)