Write the numeral in the following problem as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic.

Question

Write the numeral in the following problem as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. ​  ​

Quizplus · Accepted Answer

The given numeral uses the hexadecimal system (base 16), which includes the digits 0-9 and letters A-F to represent values from 0-15. To convert to decimal (base 10), we simply need to multiply each digit by its corresponding place value and add them together. In this case, the numeral translates to:

(1 x 16^31) + (1 x 16^30) + (10 x 16^29) + (12 x 16^28) + (9 x 16^27) + (12 x 16^26) + (12 x 16^25) + (15 x 16^24) + (8 x 16^23) + (3 x 16^22) + (4 x 16^21) + (3 x 16^20) + (8 x 16^19) + (8 x 16^18) + (4 x 16^17) + (11 x 16^16) + (11 x 16^15) + (8 x 16^14) + (4 x 16^13) + (10 x 16^12) + (7 x 16^11) + (11 x 16^10) + (3 x 16^9) + (6 x 16^8) + (3 x 16^7) + (13 x 16^6) + (3 x 16^5) + (7 x 16^4) + (5 x 16^3) + (10 x 16^2) + (11 x 16^1) + (7 x 16^0)
= 1,253,917,931,051,378,087,905,947

Rounded to the nearest whole number, this is equal to 1,254. Therefore, the correct answer is B).

Write the Numeral in the Following Problem as a Decimal