Solve for the mass of a 3.5 x 10 cg sample in units of kilograms. Click the answer you think is right. 3.5 x 10° kg 3.5 x 10° kg 3.5 x 10 kg 3.5 kg 3.5 x 10 kg
The Correct Answer and Explanation is :
Let’s break this problem down step by step to understand how to solve for the mass in kilograms.
The problem asks us to convert a mass of (3.5 \times 10^n \, \text{cg}) to kilograms. We are given a mass in centigrams (cg) and need to convert that to kilograms (kg).
Step 1: Understand the conversion factors
- Centigrams to grams:
There are 100 centigrams (cg) in 1 gram (g). So, to convert from centigrams to grams, we divide by 100:
[
1 \, \text{g} = 100 \, \text{cg} \quad \Rightarrow \quad 1 \, \text{cg} = 0.01 \, \text{g}
] - Grams to kilograms:
There are 1,000 grams (g) in 1 kilogram (kg). So, to convert from grams to kilograms, we divide by 1,000:
[
1 \, \text{kg} = 1,000 \, \text{g} \quad \Rightarrow \quad 1 \, \text{g} = 0.001 \, \text{kg}
]
Step 2: Apply the conversion
We are given (3.5 \times 10^n \, \text{cg}), and we need to convert that to kilograms.
- First, convert centigrams to grams:
[
3.5 \times 10^n \, \text{cg} \times 0.01 \, \text{g/cg} = 3.5 \times 10^n \times 0.01 \, \text{g}
]
This simplifies to:
[
3.5 \times 10^{n-2} \, \text{g}
] - Next, convert grams to kilograms:
[
3.5 \times 10^{n-2} \, \text{g} \times 0.001 \, \text{kg/g} = 3.5 \times 10^{n-2} \times 0.001 \, \text{kg}
]
This simplifies to:
[
3.5 \times 10^{n-5} \, \text{kg}
]
Step 3: Apply to the example
Let’s assume the exponent (n) in the given (3.5 \times 10^n \, \text{cg}) is 0 (which is often implied when no specific exponent is given). The calculation becomes:
[
3.5 \times 10^0 \, \text{cg} = 3.5 \, \text{cg}
]
Convert centigrams to grams:
[
3.5 \, \text{cg} = 3.5 \times 0.01 = 0.035 \, \text{g}
]
Convert grams to kilograms:
[
0.035 \, \text{g} = 0.035 \times 0.001 = 0.000035 \, \text{kg}
]
Thus, the correct mass in kilograms is (3.5 \times 10^{-5} \, \text{kg}), which is the equivalent to 0.000035 kg.
Therefore, the correct answer is:
[
3.5 \times 10^{-5} \, \text{kg}
]