Weight of Moon is `(7.345xx10^(22))` kg and weight of Earth is `(5.9724xx10^(24))` kg. What is the total weight of both in standard form?

Options

A. `(6.04xx10^(24))kg`
B. `(7.04xx10^(22))kg`
C. `(5.98xx10^(24))kg`
D. `(6.44xx10^(24))kg`

Answer

To find the total weight of the Moon and the Earth in standard form, we will follow these steps:

### Step 1: Write down the weights in standard form
The weight of the Moon is given as:
\[ W_{Moon} = 7.345 \times 10^{22} \text{ kg} \]
The weight of the Earth is given as:
\[ W_{Earth} = 5.9724 \times 10^{24} \text{ kg} \]

### Step 2: Adjust the weights to have the same power of 10
To add these two numbers, we need to express them with the same power of 10. We can convert the weight of the Moon to have the same exponent as the weight of the Earth (which is \(10^{24}\)):
\[ W_{Moon} = 7.345 \times 10^{22} = 0.07345 \times 10^{24} \]

### Step 3: Add the weights together
Now, we can add the two weights:
\[ W_{Total} = W_{Moon} + W_{Earth} \]
Substituting the values:
\[ W_{Total} = 0.07345 \times 10^{24} + 5.9724 \times 10^{24} \]
\[ W_{Total} = (0.07345 + 5.9724) \times 10^{24} \]
\[ W_{Total} = 6.04585 \times 10^{24} \]

### Step 4: Convert to standard form
The result \(6.04585 \times 10^{24}\) is already in standard form. However, we can round it to three significant figures:
\[ W_{Total} \approx 6.05 \times 10^{24} \text{ kg} \]

### Final Answer
The total weight of both the Moon and the Earth in standard form is:
\[ 6.05 \times 10^{24} \text{ kg} \]

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