Three measurements are made as 18.425 cm, 7.21 cm and 5.00 cm. The addition should be written as

Options

A. 30.635 cm
B. 30.64 cm
C. 30.63 cm
D. 30.6 cm

Answer

To solve the problem of adding the three measurements (18.425 cm, 7.21 cm, and 5.00 cm) and expressing the result with the correct number of significant figures, follow these steps:

### Step-by-Step Solution:

1. **List the Measurements**:
- The given measurements are:
- \( A = 18.425 \, \text{cm} \)
- \( B = 7.21 \, \text{cm} \)
- \( C = 5.00 \, \text{cm} \)

2. **Align the Decimal Points**:
- When adding, it's helpful to align the numbers by their decimal points:
```
18.425
+ 7.210
+ 5.000
```

3. **Perform the Addition**:
- Now, add the numbers:
\[ 18.425 + 7.210 + 5.000 = 30.635 \, \text{cm} \]

4. **Determine Significant Figures**:
- Next, we need to determine the number of significant figures in each measurement:
- \( 18.425 \) has **5 significant figures**.
- \( 7.21 \) has **3 significant figures**.
- \( 5.00 \) has **3 significant figures**.
- The result should be expressed with the least number of significant figures from the measurements, which is **3 significant figures** (from 7.21 and 5.00).

5. **Round the Result**:
- The result from the addition is \( 30.635 \, \text{cm} \).
- To round this to 3 significant figures, we look at the third significant figure (which is 6) and the next digit (which is 3):
- Since 3 is less than 5, we do not round up.
- Therefore, the rounded result is \( 30.6 \, \text{cm} \).

6. **Final Answer**:
- The final answer, expressed with the correct number of significant figures, is:
\[ \boxed{30.6 \, \text{cm}} \]