Write the numeral in the following problem as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic.
A) 1,256
B) 1,254
C) 128
D) 28
E) 100,010

Question

Write the numeral in the following problem as a decimal numeral. By decimal numeral, we mean the system we use in everyday arithmetic. ​  ​
A) 1,256 
B) 1,254 
C) 128 
D) 28 
E) 100,010

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