Match the steps to their corresponding actions in converting decimal 3000 to hexadecimal: 11 / 16 = 0, remainder 11 3000 / 16 = 187, remainder 8 187 / 16 = 11, remainder 11
Understand the Problem
The question is asking to match the steps in the process of converting the decimal number 3000 into its hexadecimal representation. The steps involve successive division by 16 and tracking the remainders, which form the hexadecimal digits.
Answer
$BB8_{16}$
Answer for screen readers
$BB8_{16}$
Steps to Solve
- Divide 3000 by 16
Divide the decimal number 3000 by 16.
$3000 \div 16 = 187$ with a remainder of $8$.
- Record the remainder
The remainder $8$ is the least significant digit (rightmost) in the hexadecimal representation.
- Divide the quotient by 16
Now, divide the quotient from the previous step (187) by 16.
$187 \div 16 = 11$ with a remainder of $11$.
- Record the remainder
The remainder $11$ corresponds to the hexadecimal digit 'B' (since A=10, B=11, C=12, D=13, E=14, F=15). This is the next digit to the left.
- Divide the quotient by 16
Divide the new quotient (11) by 16.
$11 \div 16 = 0$ with a remainder of $11$.
- Record the remainder
The remainder $11$ corresponds to the hexadecimal digit 'B'. Since the quotient is now 0, this 'B' is the most significant digit (leftmost).
- Combine the remainders
Read the remainders in reverse order of how they were obtained. Thus, $3000_{10} = BB8_{16}$.
$BB8_{16}$
More Information
Hexadecimal, or base 16, uses 16 distinct symbols, 0-9 to represent values zero to nine, and A, B, C, D, E, and F to represent values ten to fifteen. Each hexadecimal digit represents four binary digits (bits), also known as a nibble. This makes hexadecimal a compact and human-readable way to represent binary data.
Tips
A common mistake is not converting remainders greater than 9 to their corresponding hexadecimal letter (A-F). Another mistake is not reading the remainders in the correct order (from last to first).
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