To convert the binary number 1110010101 to a Hindu-Arabic number (decimal), follow these steps:

1. Start by writing the binary digits with their corresponding powers of 2: $1 \cdot 2^{9} + 1 \cdot 2^{8} + 1 \cdot 2^{7} + 0 \cdot 2^{6} + 0 \cdot 2^{5} + 1 \cdot 2^{4} + 0 \cdot 2^{3} + 1 \cdot 2^{2} + 0 \cdot 2^{1} + 1 \cdot 2^{0}$

2. Calculate the values: $(1 \cdot 512) + (1 \cdot 256) + (1 \cdot 128) + (0 \cdot 64) + (0 \cdot 32) + (1 \cdot 16) + (0 \cdot 8) + (1 \cdot 4) + (0 \cdot 2) + (1 \cdot 1)$ $= 512 + 256 + 128 + 16 + 4 + 1$

3. Sum the values: $512 + 256 + 128 + 16 + 4 + 1 = 917$

So, 1110010101 in binary is equal to 917 in the Hindu-Arabic numeral system.

Would you like further explanation on any step?

Here are 5 questions to extend your understanding:

1. How do you convert a decimal number back into binary?
2. What are the powers of 2 for the first 10 binary digits?
3. Why is binary commonly used in computer systems?
4. How would you convert the binary number to hexadecimal first?
5. Can you apply this method to any binary number length?

Tip: To quickly check your binary to decimal conversions, use the place values of powers of 2 as a guide!