Convert 0.0982 hg to its equivalent in cg.
The correct answer and explanation is :
To convert 0.0982 hectograms (hg) to centigrams (cg), follow these steps:
Step 1: Understand the metric prefixes
- Hectogram (hg) = (10^2) grams (100 g)
- Centigram (cg) = (10^{-2}) grams (0.01 g)
Since we are converting from hectograms to centigrams, we need to determine how many centigrams are in one hectogram.
1 hg = 100 g
1 g = 100 cg
So,
1 hg = (100 \times 100 = 10,000) cg
Step 2: Perform the conversion
Given: 0.0982 hg
Using the conversion factor:
[
0.0982 \times 10,000 = 982 \text{ cg}
]
Final Answer:
0.0982 hg = 982 cg
Detailed Explanation (300 words)
The metric system is based on powers of ten, making unit conversion straightforward. The prefixes indicate the scale relative to the base unit, which in this case is the gram (g).
- A hectogram (hg) is 100 grams, meaning it is a larger unit.
- A centigram (cg) is 1/100 of a gram, meaning it is a smaller unit.
To convert from a larger unit (hectograms) to a smaller unit (centigrams), we multiply by the appropriate power of ten. Since there are 10,000 centigrams in a hectogram, multiplying 0.0982 by 10,000 gives us 982 centigrams.
This conversion is crucial in fields like chemistry, medicine, and food science, where precise measurements are needed. For example, a dietitian might convert food weights from hectograms to centigrams to better quantify nutrient intake, or a pharmacist might use similar conversions for medication dosages.
By understanding the metric system, we can easily move between different units by shifting the decimal point. This simplicity is one reason the metric system is used worldwide for scientific and everyday measurements.
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