A pencil has a length of 9.2 cm. It is broken into two pieces. If the smaller piece has a length of 4.46 cm, what is the length of the larger piece?

Answer

To find the length of the larger piece of the pencil after it has been broken, we can follow these steps:

### Step 1: Understand the total length of the pencil
The total length of the pencil is given as 9.2 cm.

### Step 2: Identify the length of the smaller piece
The length of the smaller piece is given as 4.46 cm.

### Step 3: Set up the equation
Let the length of the larger piece be represented as \( L_1 \). According to the problem, the sum of the lengths of the two pieces equals the total length of the pencil:
\[ L_1 + 4.46 \text{ cm} = 9.2 \text{ cm} \]

### Step 4: Solve for the length of the larger piece
To find \( L_1 \), we can rearrange the equation:
\[ L_1 = 9.2 \text{ cm} - 4.46 \text{ cm} \]

### Step 5: Perform the subtraction
Now, we will subtract the lengths:
\[ L_1 = 9.2 - 4.46 \]
To perform the subtraction, we can align the decimal points:
```
9.20
- 4.46
-------
```
Calculating this gives:
\[ L_1 = 4.74 \text{ cm} \]

### Step 6: Apply significant figures
Since the measurement of the pencil's length is given to one decimal place (9.2 cm), we should round our answer to one decimal place as well. Thus, we round 4.74 cm to 4.7 cm.

### Final Answer
The length of the larger piece is **4.7 cm**.

---