Final answer:
The binary representation of the decimal number 2010 is found by repeatedly dividing by 2 and recording the remainders. Reading the remainders in reverse order, we get 11111010010, which is option 1.
Step-by-step explanation:
To convert the number 2010 from base 10 to base 2, we use a process of dividing the number by 2 and recording the remainders. We continue this process until we reach a quotient of 0. The remainders, read in reverse order, give us the binary representation of the number.
Divide 2010 by 2, which gives us a quotient of 1005 and a remainder of 0. Our binary number ends in 0.
Divide 1005 by 2, which gives us a quotient of 502 and a remainder of 1. Our binary number now ends in 10.
Continue this process until the quotient is 0.
When we finish this process, we find that the binary representation of 2010 is 11111010010, which corresponds to option 1.