Why is the decimal number 2 written as 10 in binary?

In the binary number system, the decimal number 2 is written as 10 because binary is a positional system with a base of 2.12

In a positional numeral system, the value of a digit depends on its position, which corresponds to powers of the base. In the decimal system, the base is 10, so the number 10 represents one unit of the first power of 10 ($1\times {10}^1$) plus zero units of the zeroth power ($0\times {10}^0$).34

Similarly, in the binary system, the base is 2. The number 2 is represented as 10 because it consists of one unit of the first power of 2 ($1\times 2^1$) and zero units of the zeroth power ($0\times 2^0$). Essentially, the binary "10" plays the same role in base 2 that "10" plays in the decimal system, marking the transition to the next positional value.42