Three pieces of silver have masses 2.3 kg, 41.15g and 30.19g. The total mass of correct significant figures is 

Options

A. `2.37032 kg `
B. `2.370 kg`
C. `2.37 kg`
D. `2.4 kg`

Answer

To solve the problem of finding the total mass of three pieces of silver with the correct significant figures, we will follow these steps:

### Step 1: Convert all masses to the same unit
We have three masses:
- \( m_1 = 2.3 \, \text{kg} \)
- \( m_2 = 41.15 \, \text{g} \)
- \( m_3 = 30.19 \, \text{g} \)

We need to convert \( m_2 \) and \( m_3 \) from grams to kilograms.

\[ m_2 = 41.15 \, \text{g} = 41.15 \times 10^{-3} \, \text{kg} = 0.04115 \, \text{kg} \]

\[ m_3 = 30.19 \, \text{g} = 30.19 \times 10^{-3} \, \text{kg} = 0.03019 \, \text{kg} \]

### Step 2: Add the masses together
Now we can add all three masses together:

\[ m = m_1 + m_2 + m_3 \]

Substituting the values:

\[ m = 2.3 \, \text{kg} + 0.04115 \, \text{kg} + 0.03019 \, \text{kg} \]

Calculating this step-by-step:

\[ m = 2.3 + 0.04115 + 0.03019 \]

First, add \( 0.04115 + 0.03019 \):

\[ 0.04115 + 0.03019 = 0.07134 \]

Now add this to \( 2.3 \):

\[ m = 2.3 + 0.07134 = 2.37134 \, \text{kg} \]

### Step 3: Determine the correct significant figures
Now we need to round the result to the correct number of significant figures.

- \( m_1 = 2.3 \, \text{kg} \) has **2 significant figures**.
- \( m_2 = 41.15 \, \text{g} \) has **4 significant figures**.
- \( m_3 = 30.19 \, \text{g} \) has **4 significant figures**.

The least number of decimal places among these is from \( m_1 \), which has **1 decimal place**. Therefore, we will round \( 2.37134 \, \text{kg} \) to **1 decimal place**.

Rounding \( 2.37134 \) to 1 decimal place gives:

\[ 2.4 \, \text{kg} \]

### Final Answer
The total mass of the three pieces of silver, expressed with the correct significant figures, is:

\[ \boxed{2.4 \, \text{kg}} \]