Answer

Decimal $108.25_{10} = \mathbf{1101100.01_2}$

Explanation

We convert integer and fractional parts separately.

1. Integer part: $108_{10}$ → binary

Use repeated division by 2:

Division	Quotient	Remainder
108 ÷ 2	54	0
54 ÷ 2	27	0
27 ÷ 2	13	1
13 ÷ 2	6	1
6 ÷ 2	3	0
3 ÷ 2	1	1
1 ÷ 2	0	1

Reading remainders bottom → top:
$$108_{10} = 1101100_2$$
Verification: $1\cdot64 +1\cdot32 +0\cdot16 +1\cdot8 +1\cdot4 +0\cdot2 +0\cdot1 = 108$.

2. Fractional part: $0.25_{10}$ → binary

Repeated multiplication by 2:

• $0.25 \times 2 = 0.50$ → 0
• $0.50 \times 2 = 1.00$ → 1 → terminate (fraction = 0)

Reading integers top → bottom:
$$0.25_{10} = 0.01_2$$

3. Combine

$$108.25_{10} = 1101100.01_2$$

Check

$1101100.01_2 = 64+32+8+4 + 0/2 +1/4 =108 +0.25 =108.25$ ✓

Final Answer

$$\mathbf{108.25_{10} = 1101100.01_2}$$