| Decimal | Base 3 | Why? | |---------|--------|------| | 0 | 0 | | | 1 | 1 | | | 2 | 2 | | | 3 | 10 | (1 \times 3 + 0) | | 4 | 11 | (3 + 1) | | 5 | 12 | (3 + 2) | | 6 | 20 | (2 \times 3 + 0) | | 7 | 21 | (6 + 1) | | 8 | 22 | (6 + 2) | | 9 | 100 | (1 \times 9 + 0 + 0) | | 10 | 101 | (9 + 1) | | 11 | 102 | (9 + 2) | | 12 | 110 | (9 + 3) | | … | … | | Method: Repeated division by 3, reading remainders bottom to top .
( 1022_3 ) [ 1 \times 27 + 0 \times 9 + 2 \times 3 + 2 \times 1 = 27 + 0 + 6 + 2 = 35_10 ] 6. Arithmetic in Base 3 Addition Add digit by digit, carry when sum ≥ 3. base 3
Check: ( 2 \times 9 + 2 \times 3 + 1 = 18 + 6 + 1 = 25 ). Multiply each digit by its place value (power of 3) and sum. | Decimal | Base 3 | Why