`12.63 - 10.2 = 2.34 ~~ 2.4 `

Answer

To solve the problem \( 12.63 - 10.2 \) and round the answer appropriately based on significant figures, we can follow these steps:

### Step 1: Perform the subtraction
First, we need to subtract the two numbers:
\[ 12.63 - 10.2 \]
Aligning the numbers for clarity:
```
12.63
- 10.20
--------
```
Now, we perform the subtraction:
\[ 12.63 - 10.20 = 2.43 \]

### Step 2: Determine the number of significant figures
Next, we need to determine how many significant figures we should keep in our final answer.

- The number \( 12.63 \) has **two decimal places** (the digits after the decimal are 6 and 3).
- The number \( 10.2 \) has **one decimal place** (the digit after the decimal is 2).

### Step 3: Identify the limiting factor
In subtraction, the result should be reported with the same number of decimal places as the number with the **least** decimal places. Here, \( 10.2 \) has the least decimal places (1 decimal place).

### Step 4: Round the result
Now, we round our result \( 2.43 \) to **one decimal place**:
- The digit in the tenths place is 4, and the digit in the hundredths place is 3. Since the hundredths place (3) is less than 5, we do not round up.
- Thus, \( 2.43 \) rounded to one decimal place is \( 2.4 \).

### Final Answer
The final answer is:
\[ 2.4 \]