Questions: Convert the numeral to a numeral in base 10. B 8212=square10

Convert the numeral to a numeral in base 10. B 8212=square10
Transcript text: Convert the numeral to a numeral in base 10. \[ \mathrm{B} 82_{12}=\square_{10} \]
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Solution

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Solution Steps

Step 1: Understand the numeral system

The numeral \(\mathrm{B}82_{12}\) is in base 12. In base 12, the digits range from 0 to 11, where \(\mathrm{B}\) represents 11 in base 10.

Step 2: Break down the numeral

The numeral \(\mathrm{B}82_{12}\) can be expanded as: \[ \mathrm{B} \times 12^2 + 8 \times 12^1 + 2 \times 12^0 \]

Step 3: Substitute the values

Substitute \(\mathrm{B} = 11\) and calculate each term: \[ 11 \times 12^2 = 11 \times 144 = 1584 \] \[ 8 \times 12^1 = 8 \times 12 = 96 \] \[ 2 \times 12^0 = 2 \times 1 = 2 \]

Step 4: Sum the terms

Add the results of the three terms: \[ 1584 + 96 + 2 = 1682 \]

Final Answer

\[ \boxed{1682_{10}} \]

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