convert 689 base 10 to base 3. Can you please show me this step by step
sure. take the powers of 3
3,9,27,81,243
so in base 10 689, I see
two 243 (486) plus
two 81 (162) we are up to 648 now, or 41 left, so
one 27 (27)
one 9 (9)
one 3 (3)
and two remainders.
in inverse order the number base 3 is
2111222
in regular order
2211122
check
2*3^0= 2
1*3^1= 3
1*3^2= 9
1*3^3= 27
2*3^4= 162
2*3^5= 486
base10 total= sum of above 689
To convert a number from base 10 to base 3, follow these steps:
Step 1: Start with the given decimal number, 689.
Step 2: Divide the number by the base (3) and write down the quotient and remainder.
689 ÷ 3 = 229 remainder 2
Write down the remainder in the rightmost position.
Step 3: Divide the quotient obtained in Step 2 by the base (3) again.
229 ÷ 3 = 76 remainder 1
Write down the remainder next to the previous remainder.
Step 4: Repeat Step 3 with the new quotient obtained.
76 ÷ 3 = 25 remainder 1
Write down the remainder next to the previous remainders.
Step 5: Continue this process until the quotient becomes 0.
25 ÷ 3 = 8 remainder 1
8 ÷ 3 = 2 remainder 2
2 ÷ 3 = 0 remainder 2
Step 6: Write down the final remainders from left to right.
The final remainders are: 2 2 1 1 1 2.
Step 7: Read the final remainders from right to left to get the converted number.
The base-3 representation of 689 is 221112.