Three measurements are made as 18.425 cm, 7.21 cm and 5.0 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 5.0 cm) and expressing the result with the correct number of significant figures, we can follow these steps:

### Step 1: Add the Measurements
We start by adding the three measurements together:

1. **First Measurement:** 18.425 cm
2. **Second Measurement:** 7.21 cm
3. **Third Measurement:** 5.0 cm

Now, we perform the addition:
\[ 18.425 + 7.21 + 5.0 \]

Calculating step by step:
- Add 18.425 and 7.21:
\[ 18.425 + 7.21 = 25.635 \]
- Now add the result to 5.0:
\[ 25.635 + 5.0 = 30.635 \]

So, the total sum is:
\[ 30.635 \text{ cm} \]

### Step 2: Determine Significant Figures
Next, we need to round the result based on the significant figures of the measurements involved.

- **18.425 cm** has **5 significant figures**.
- **7.21 cm** has **3 significant figures**.
- **5.0 cm** has **2 significant figures**.

The rule for addition states that the result should be rounded to the least number of decimal places of the measurements being added.

- The measurement with the least decimal places is **5.0 cm**, which has **1 decimal place**.

### Step 3: Round the Result
Now we round the total sum (30.635 cm) to **1 decimal place**:
- The first decimal place in 30.635 is **6** (in the tenths place).
- The second decimal place is **3** (in the hundredths place), which is less than 5, so we do not round up.

Thus, rounding 30.635 cm to 1 decimal place gives us:
\[ 30.6 \text{ cm} \]

### Final Answer
The addition of the three measurements should be written as:
\[ \boxed{30.6 \text{ cm}} \]