Solve for the mass of 3.5 105 cg sample In units of kilograms Click the answer you think Is right 3.5 x 10*kg 3.5 * 108kg 3.5x 10″kg 3.5kg 3.5 * 10″ kg
The Correct Answer and Explanation is:
To solve for the mass of a 3.5 × 10⁵ centigram (cg) sample in kilograms (kg), begin by converting centigrams to kilograms using standard metric conversions:
- Conversion factors:
- 1 kilogram (kg) = 1,000 grams (g)
- 1 gram (g) = 100 centigrams (cg)
- Step-by-step conversion:
First, convert centigrams to grams: 3.5×105 cg÷100=3.5×103 g3.5 \times 10^5\ \text{cg} \div 100 = 3.5 \times 10^3\ \text{g}3.5×105 cg÷100=3.5×103 g Next, convert grams to kilograms: 3.5×103 g÷1000=3.5 kg3.5 \times 10^3\ \text{g} \div 1000 = 3.5\ \text{kg}3.5×103 g÷1000=3.5 kg
Therefore, the mass of the sample is 3.5 kilograms.
Correct answer: 3.5 kg
Explanation:
This problem involves converting a metric mass unit across different scales. The centigram is a much smaller unit compared to the kilogram. Since 1 kilogram contains 100,000 centigrams (because 1 kg = 1000 g and 1 g = 100 cg, so 1000 × 100 = 100,000), it becomes essential to apply the correct conversion ratios systematically.
By first reducing the value from centigrams to grams, then from grams to kilograms, the calculation becomes more manageable and less prone to error. Understanding this two-step process helps prevent misinterpretation of scientific notation or confusion between metric prefixes.
The scientific notation used, 3.5 × 10⁵, shows that the number of centigrams is quite large. However, when expressed in kilograms, it simplifies to 3.5, showing how the mass is moderate in size when viewed in a larger unit.
No need for approximation in this case; exact unit conversions yield a precise and clear result.
