Question:
Convert the number 1982 from base 10 to base 12. The result is:
Convert the number 1982 from base 10 to base 12. The result is:
Show Hint
Divide repeatedly by 12 (or use the powers 1728, 144, 12) and read off the digits.
Updated On: Nov 4, 2026
- 1182
- 1912
- 1192
- 1292
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Use powers of 12.
\( 12^3 = 1728 \) and \( 12^2 = 144 \).
Step 2: Extract digits.
\( 1982 = 1 \times 1728 + 254 \)
\( 254 = 1 \times 144 + 110 \)
\( 110 = 9 \times 12 + 2 \)
Step 3: Write the digits.
From \( 12^3 \) down to \( 12^0 \) the digits are 1, 1, 9, 2, so \( 1982_{10} = 1192_{12} \).
Step 4: Check.
\( 1\cdot1728 + 1\cdot144 + 9\cdot12 + 2 = 1728+144+108+2 = 1982 \).
Final Answer:
The correct option is (3): 1192
\( 12^3 = 1728 \) and \( 12^2 = 144 \).
Step 2: Extract digits.
\( 1982 = 1 \times 1728 + 254 \)
\( 254 = 1 \times 144 + 110 \)
\( 110 = 9 \times 12 + 2 \)
Step 3: Write the digits.
From \( 12^3 \) down to \( 12^0 \) the digits are 1, 1, 9, 2, so \( 1982_{10} = 1192_{12} \).
Step 4: Check.
\( 1\cdot1728 + 1\cdot144 + 9\cdot12 + 2 = 1728+144+108+2 = 1982 \).
Final Answer:
The correct option is (3): 1192
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