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Express 249 11 3ab 12 as a base 10 integer. Here a and b denote the digits whose values are 10 and 11, respectively, in base 12.

a) 3745
b)3747
c) 3737
d) 3755

1 Answer

6 votes

Final answer:

To convert the base 12 number 249 11 3ab 12 to base 10, we expand each digit by its place value and sum them, with 'a' valued at 10 and 'b' at 11. The conversion totals 583790 + 11/12; however, none of the provided answer choices match this total, indicating a potential error in the question or answer choices.

Step-by-step explanation:

The student is asking to convert a number from base 12 to a base 10 integer. In base 12, 'a' represents the value 10 and 'b' represents the value 11. To convert the number 249 11 3ab 12 into a base 10 integer, we can expand it by its place values:

  • (2 × 12^5) = 2 × 248832 = 497664
  • (4 × 12^4) = 4 × 20736 = 82944
  • (9 × 12^3) = 9 × 1728 = 15552
  • (11 × 12^2) = 11 × 144 = 1584
  • (3 × 12^1) = 3 × 12 = 36
  • (10 × 12^0) = 10 × 1 = 10
  • (11 × 12^-1) = 11/12

When you sum these values, you get the total in base 10:


497664 + 82944 + 15552 + 1584 + 36 + 10 + 11/12 =

583790 + 11/12

Since we cannot have a fraction in an integer, we exclude the 11/12 yielding the final answer as 583790. Therefore, none of the options given a) 3745 b) 3747 c) 3737 d) 3755 match the correct conversion.

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