 what base 10 number does 101.1101
 represent? 

The binary number \(101.1101_2\) can be converted to a base 10 number by considering the place values of each digit.

### Steps for Conversion:

#### Integer Part:
The integer part is \(101_2\), which represents:
\[
1 \times 2^2 + 0 \times 2^1 + 1 \times 2^0 = 4 + 0 + 1 = 5
\]

#### Fractional Part:
The fractional part is \(0.1101_2\), where each digit corresponds to negative powers of 2:
\[
1 \times 2^{-1} + 1 \times 2^{-2} + 0 \times 2^{-3} + 1 \times 2^{-4}
\]
\[
= \frac{1}{2} + \frac{1}{4} + 0 + \frac{1}{16}
\]
\[
= 0.5 + 0.25 + 0 + 0.0625 = 0.8125
\]

#### Combining Both Parts:
\[
101.1101_2 = 5 + 0.8125 = 5.8125_{10}
\]

Thus, the binary number \(101.1101_2\) is equal to \(5.8125_{10}\) in decimal.

Would you like further clarification on any step?

### Related Questions:
1. How do you convert a binary number with more fractional digits to decimal?
2. What is the base-10 representation of \(1101.101_2\)?
3. How does binary representation work in computer systems?
4. What is the significance of base-2 (binary) in computing?
5. Can you explain the conversion process for octal and hexadecimal numbers to base 10?

### Tip:
When converting from binary to decimal, remember that the integer part uses positive powers of 2, while the fractional part uses negative powers of 2.

What base 10 number does 101.1101 represent?

Convert the binary number 101.1101 to its decimal equivalent with this step-by-step guide. Learn how to apply place value and powers of 2 for both integer and fractional parts, making this suitable for high school students in Grades 9-12.

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