Compare XXII₁₂ (using >,<,=)

• A. >
• B. <<
• C. =
• D. None

To compare the number XXII₁₂, which is in base 12, we first need to convert it to base 10. In base 12, the digits represent powers of 12. Here, XXII₁₂ can be broken down as follows:

Conversion to Base 10

Each digit corresponds to a power of 12:

• X (10 in base 10) at the 12^1 place: 10 × 12^1 = 120
• X (10 in base 10) at the 12^0 place: 10 × 12^0 = 10
• I (1 in base 10) at the 12^-1 place: 1 × 12^-1 = 0.0833

Now, adding these values together:

120 + 10 + 0.0833 = 130.0833

Comparison with Other Values

Now, let's compare XXII₁₂ (which is approximately 130.0833 in base 10) with other values:

• A. 130
• B. 131
• C. 130.0833
• D. None

Results of the Comparison

Based on the conversion:

• XXII₁₂ > A (130) because 130.0833 is greater than 130.
• XXII₁₂ < B (131) because 130.0833 is less than 131.
• XXII₁₂ = C (130.0833) because they are equal.
• XXII₁₂ is not None.

In summary, the comparisons yield:

• XXII₁₂ > A
• XXII₁₂ < B
• XXII₁₂ = C
• XXII₁₂ is not None