Use division to convert the base ten numeral 35 to base five.
Divide successively by 5 and put the remainder on the right:
35 | 0
7 | 2
1
Read from the bottom towards the top to get
3510 = 1205
To convert a base ten numeral (in this case, 35) to a different base (in this case, base five) using division, follow these steps:
Step 1: Divide the decimal number by the new base (5) to find the quotient and remainder.
35 ÷ 5 = 7 with a remainder of 0
Step 2: Write down the remainder. This will be the least significant digit of the new base number.
Remainder: 0
Step 3: Divide the quotient obtained in the previous step by the new base (5) again.
7 ÷ 5 = 1 with a remainder of 2
Step 4: Write down the remainder obtained in the previous step. This will be the next digit (to the left) in the base number.
Remainder: 2
Step 5: Repeat steps 3 and 4 until the quotient becomes zero.
1 ÷ 5 = 0 with a remainder of 1
Remainder: 1
Since the quotient is now zero, we have obtained all the remainders needed to write the base five representation.
Step 6: Write down the remainders in reverse order.
Starting from the last remainder we obtained and moving towards the first remainder, we have: 102.
Therefore, the base ten numeral 35 in base five is equal to 102.