Two gold pieces, each of mass 0.035 g are placed in a box of mass 2.3 g. The total mass of the box with gold pieces is

Options

A. 2.3 g
B. 2.4 g
C. 2.37 g
D. 2.370 g

Answer

To solve the problem of finding the total mass of a box with two gold pieces, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Mass of the Box**:
The mass of the box is given as 2.3 g.

2. **Identify the Mass of the Gold Pieces**:
Each gold piece has a mass of 0.035 g, and there are two pieces. Therefore, the total mass of the gold pieces can be calculated as:
\[ \text{Total mass of gold} = 2 \times 0.035 \, \text{g} = 0.070 \, \text{g} \]

3. **Calculate the Total Mass**:
Now, we add the mass of the box and the total mass of the gold pieces:
\[ \text{Total mass} = \text{Mass of box} + \text{Total mass of gold} = 2.3 \, \text{g} + 0.070 \, \text{g} = 2.370 \, \text{g} \]

4. **Determine Significant Figures**:
We need to consider the significant figures in our final answer. The mass of the box (2.3 g) has 2 significant figures, while the total mass of the gold (0.070 g) has 3 significant figures. According to the rules of significant figures, the result should be reported with the least number of significant figures from the values being added, which is 2 significant figures.

5. **Round the Total Mass**:
The calculated total mass is 2.370 g. When rounding this to 2 significant figures, we look at the first two digits (2.3) and the next digit (7). Since 7 is greater than 5, we round up:
\[ \text{Rounded total mass} = 2.4 \, \text{g} \]

### Final Answer:
The total mass of the box with the gold pieces is **2.4 g**.

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