Convert `0.454545` to binary equivalent.

Answer

To convert the decimal number `0.454545` to its binary equivalent, we will follow the method of multiplying by 2 and recording the integer part. Here’s a step-by-step solution:

### Step 1: Multiply by 2
Multiply `0.454545` by `2`:
\[ 0.454545 \times 2 = 0.90909 \]
The integer part is `0`.

### Step 2: Record the integer part
Record the integer part (`0`) and take the fractional part (`0.90909`) for the next multiplication.

### Step 3: Repeat the multiplication
Multiply the fractional part `0.90909` by `2`:
\[ 0.90909 \times 2 = 1.81818 \]
The integer part is `1`.

### Step 4: Record the integer part
Record the integer part (`1`) and take the fractional part (`0.81818`) for the next multiplication.

### Step 5: Continue the process
Multiply the fractional part `0.81818` by `2`:
\[ 0.81818 \times 2 = 1.63636 \]
The integer part is `1`.

### Step 6: Record the integer part
Record the integer part (`1`) and take the fractional part (`0.63636`) for the next multiplication.

### Step 7: Repeat
Multiply the fractional part `0.63636` by `2`:
\[ 0.63636 \times 2 = 1.27272 \]
The integer part is `1`.

### Step 8: Record the integer part
Record the integer part (`1`) and take the fractional part (`0.27272`) for the next multiplication.

### Step 9: Continue
Multiply the fractional part `0.27272` by `2`:
\[ 0.27272 \times 2 = 0.54544 \]
The integer part is `0`.

### Step 10: Record the integer part
Record the integer part (`0`) and take the fractional part (`0.54544`) for the next multiplication.

### Step 11: Repeat
Multiply the fractional part `0.54544` by `2`:
\[ 0.54544 \times 2 = 1.09088 \]
The integer part is `1`.

### Step 12: Record the integer part
Record the integer part (`1`) and take the fractional part (`0.09088`) for the next multiplication.

### Step 13: Continue
Multiply the fractional part `0.09088` by `2`:
\[ 0.09088 \times 2 = 0.18176 \]
The integer part is `0`.

### Step 14: Record the integer part
Record the integer part (`0`) and take the fractional part (`0.18176`) for the next multiplication.

### Step 15: Repeat
Multiply the fractional part `0.18176` by `2`:
\[ 0.18176 \times 2 = 0.36352 \]
The integer part is `0`.

### Step 16: Record the integer part
Record the integer part (`0`) and take the fractional part (`0.36352`) for the next multiplication.

### Step 17: Continue
Multiply the fractional part `0.36352` by `2`:
\[ 0.36352 \times 2 = 0.72704 \]
The integer part is `0`.

### Step 18: Record the integer part
Record the integer part (`0`) and take the fractional part (`0.72704`) for the next multiplication.

### Step 19: Repeat
Multiply the fractional part `0.72704` by `2`:
\[ 0.72704 \times 2 = 1.45408 \]
The integer part is `1`.

### Step 20: Record the integer part
Record the integer part (`1`) and take the fractional part (`0.45408`) for the next multiplication.

### Final Step: Compile the results
Now, we compile all the integer parts we've recorded:
- From Step 1: `0`
- From Step 3: `1`
- From Step 5: `1`
- From Step 7: `1`
- From Step 9: `0`
- From Step 11: `1`
- From Step 13: `0`
- From Step 15: `0`
- From Step 17: `0`
- From Step 19: `1`

Thus, the binary equivalent of `0.454545` is:
\[ 0.0111010001... \text{ (and it continues)} \]