10100010010

10100010010 is a binary number. In the decimal system, this binary representation translates to the number 1300. Binary numbers are base-2 numeral systems, meaning they only use two digits: 0 and 1. Each digit's position in a binary number represents a power of 2, starting from the rightmost digit as 2 to the power of 0, then 2 to the power of 1, and so on. To convert 10100010010 from binary to decimal, we multiply each digit by its corresponding power of 2 and sum the results.

Starting from the rightmost digit:

0 * 2^0 = 0

1 * 2^1 = 2

0 * 2^2 = 0

0 * 2^3 = 0

1 * 2^4 = 16

0 * 2^5 = 0

0 * 2^6 = 0

0 * 2^7 = 0

1 * 2^8 = 256

0 * 2^9 = 0

1 * 2^10 = 1024

Summing these values: 0 + 2 + 0 + 0 + 16 + 0 + 0 + 0 + 256 + 0 + 1024 = 1300. Therefore, 10100010010 in binary is equivalent to 1300 in decimal. Binary numbers are fundamental in computer science and digital electronics, forming the basis of how computers process and store information.