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
I see you're working on converting decimal numbers to different bases. Let's go through your work for converting 164_10 to octal and hexadecimal. Decimal to Octal Conversion (164_10 to Octal) To convert a decimal number to octal, we repeatedly divide the decimal number by 8 and record the remainders. Step 1: Divide 164 by 8. 164 ÷ 8 = 20 with a remainder of 4. (Your work shows a remainder of 6, which is incorrect. 8 × 20 = 160, so 164 - 160 = 4.) Step 2: Divide the quotient (20) by 8. 20 ÷ 8 = 2 with a remainder of 4. Step 3: Divide the quotient (2) by 8. 2 ÷ 8 = 0 with a remainder of 2. Now, read the remainders from bottom to top: 2, 4, 4. So, 164_10 = 244_8. Your answer of (24)_8 is incorrect because of the error in the first division's remainder. The final answer is 244_8. Decimal to Hexadecimal Conversion (164_10 to Hexadecimal) To convert a decimal number to hexadecimal, we repeatedly divide the decimal number by 16 and record the remainders. Remember that remainders 10-15 are represented by letters A-F. Step 1: Divide 164 by 16. 164 ÷ 16 = 10 with a remainder of 4. (Your work shows a quotient of 2, which is incorrect. 16 × 10 = 160, so 164 - 160 = 4.) Step 2: Divide the quotient (10) by 16. 10 ÷ 16 = 0 with a remainder of 10. In hexadecimal, the digit 10 is represented by 'A'. Now, read the remainders from bottom to top: A, 4. So, 164_10 = A4_16. Your answer of (24)_16 is incorrect because of the error in the first division's quotient and the resulting hexadecimal digit. The final answer is A4_16. You've completed 5 questions now. What's next? 📸