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

329 to base six

Find the greatest power of 6 that is less than or equal to 329.

6^0 = 1
6^1 = 6
6^2 = 36
6^3 = 216
6^4 = 1296

So you need to start with 6^3.

Divide 329 by 216, then take the remainder and go to the next lowest power.

329 / 216 = 1 R 113

Now divide 113 by 6^2

113 / 36 = 3 R 5

Now divide 5 by 6^1

5 / 6 = 0 R 5

Now divide 5 by 6^0

5 / 1 = 5 R 0

Using the quotients, the number in base 6 is 1305.

You can also do this the other way around. Compute the last digit by taking the remainder after division by 6:

329 mod 6 = 5

Subtract 5 and divide by 6 to obtain:

(329 - 5)/6 = 54

Then the first digit of 54 in base 6 will be the next digit. So, we can just iterate the process with 329 replaced by 54:

54 mod 6 = 0 : next digit is 0

54/6 = 9

9 Mod 6 = 3 : next digit is 3

(9 - 3)/6 = 1 which is simply 1 in base 6, so the last digit is 1.

Why did the tomato go to the party?

Because it couldn't find a date!

Now, let's convert 329 to base six.

To convert a base-ten number to base six, we need to divide the number by six repeatedly and keep track of the remainders.

329 divided by 6 is 54 with a remainder of 5.
54 divided by 6 is 9 with a remainder of 0.
9 divided by 6 is 1 with a remainder of 3.
1 divided by 6 is 0 with a remainder of 1.

Putting these remainders together in reverse order, we get 1035 in base six.

To convert the base-ten number 329 to base six, follow these steps:

Step 1: Divide the given decimal number by the base (six) to get the quotient and remainder.
329 ÷ 6 = 54 remainder 5

Step 2: Take note of the remainder in step 1 as the least significant digit in the base-six numeral.
In this case, the remainder is 5, so the least significant digit is 5.

Step 3: Divide the quotient obtained in step 1 by the base (six) again.
54 ÷ 6 = 9 remainder 0

Step 4: Take note of the remainder in step 3 as the next digit in the base-six numeral.
In this case, the remainder is 0, so the next digit is 0.

Step 5: Repeat steps 3 and 4 until the quotient is zero.
9 ÷ 6 = 1 remainder 3
1 ÷ 6 = 0 remainder 1

Step 6: Take note of the remainders obtained in each step, starting from the last one, to form the remaining digits of the base-six numeral.
In this case, the remainders are 1, 3, and 5, so the remaining digits are 153.

Therefore, the base-ten number 329 is equivalent to the base-six numeral 153.

To convert a base-ten number to a numeral in another base, you need to follow these steps:

1. Divide the given number by the base you want to convert it to (in this case, base six).
2. Write down the remainder of the division as a digit in the new base.
3. If the quotient is greater than zero, divide it by the base again and repeat step 2.
4. Continue repeating steps 2 and 3 until the quotient becomes zero.
5. Write down the digits obtained from the remainders in reverse order to get the numeral in the new base.

Let's apply these steps to convert 329 to base six:

Step 1:
Divide 329 by 6. The quotient is 54, and the remainder is 5.

Step 2:
Write down the remainder (5) as a digit in base six.

Step 3:
Divide the quotient (54) by 6. The new quotient is 9, and the remainder is 0.

Step 4:
Since the quotient is now zero, we stop dividing.

Step 5:
The digits obtained from the remainders in reverse order are 05.

Therefore, 329 in base ten is equal to 05 in base six.