Convert the binary number 101101101 to its decimal equivalent.

To convert the binary number \( 101101101 \) to decimal, we interpret each binary digit as a power of 2, starting from the right (the least significant bit).

The binary number \( 101101101 \) can be expanded as follows:

\[
1 \times 2^8 + 0 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0
\]

Calculating each term:

\[
1 \times 2^8 = 256
\]
\[
0 \times 2^7 = 0
\]
\[
1 \times 2^6 = 64
\]
\[
1 \times 2^5 = 32
\]
\[
0 \times 2^4 = 0
\]
\[
1 \times 2^3 = 8
\]
\[
1 \times 2^2 = 4
\]
\[
0 \times 2^1 = 0
\]
\[
1 \times 2^0 = 1
\]

Now, adding these values:

\[
256 + 0 + 64 + 32 + 0 + 8 + 4 + 0 + 1 = 365
\]

So, the decimal equivalent of the binary number \( 101101101 \) is:

\[
\boxed{365}
\]

Would you like details on any step? 

Here are 5 related questions:
1. How would you convert a decimal number to binary?
2. What is the binary representation of the decimal number 500?
3. How can binary numbers be used in computer science?
4. Why does each digit in binary represent a power of 2?
5. How do you convert hexadecimal numbers to binary?

**Tip:** Remember, each digit in binary represents an increasing power of 2, starting from the right.

Discover how to convert the binary number 101101101 into its decimal equivalent, step-by-step. This problem introduces binary number system concepts and demonstrates the process of binary-to-decimal conversion, suitable for Grades 6-8.

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