This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To express the sum in base six, we first convert each number to base 10, then add them, and finally convert the sum to base six. Step 1: Convert 112012_three to base 10. 112012_three = 1 × 3^5 + 1 × 3^4 + 2 × 3^3 + 0 × 3^2 + 1 × 3^1 + 2 × 3^0 = 1 × 243 + 1 × 81 + 2 × 27 + 0 × 9 + 1 × 3 + 2 × 1 = 243 + 81 + 54 + 0 + 3 + 2 = 383_ten Step 2: Convert 21(21)_four to base 10. Assuming 21(21)_four means 2121_four (as is common for number base notation where digits are listed sequentially). 2121_four = 2 × 4^3 + 1 × 4^2 + 2 × 4^1 + 1 × 4^0 = 2 × 64 + 1 × 16 + 2 × 4 + 1 × 1 = 128 + 16 + 8 + 1 = 153_ten Step 3: Find the sum of the two numbers in base 10. Sum = 383_ten + 153_ten Sum = 536_ten Step 4: Convert 536_ten to base six. We use repeated division by 6 and record the remainders. 536 ÷ 6 = 89 remainder 2 89 ÷ 6 = 14 remainder 5 14 ÷ 6 = 2 remainder 2 2 ÷ 6 = 0 remainder 2 Reading the remainders from bottom to top, we get 2252_six. The sum of 112012_three and 21(21)_four in base six is: 2252_six Drop the next question.