How many mg are equal to 450 µg? 1 9. How many mm are equal to 0.003 dm?
The Correct Answer and Explanation is:
Answers:
- 450 µg = 0.45 mg
- 0.003 dm = 0.3 mm
Explanation (300 words):
Understanding unit conversions is a fundamental aspect of science and everyday life, especially when dealing with measurements in fields like medicine, physics, and engineering. Let’s break down both problems to see how the conversions work and why the answers are correct.
1. Converting Micrograms (µg) to Milligrams (mg):
The metric system is based on powers of 10. Here are the relevant prefixes:
- Micro (µ) means one-millionth, or 10−610^{-6}
- Milli (m) means one-thousandth, or 10−310^{-3}
So to convert micrograms to milligrams, we move three decimal places to the left, because a milligram is 1,000 times larger than a microgram. 450 μg=450÷1,000=0.45 mg450\ \mu g = 450 \div 1,000 = 0.45\ mg
Hence, 450 micrograms equals 0.45 milligrams.
This conversion is commonly used in pharmacology. For instance, many drug dosages are prescribed in micrograms but need to be prepared or compared in milligrams.
2. Converting Decimeters (dm) to Millimeters (mm):
Let’s look at the relationships between metric units of length:
- 1 decimeter (dm) = 100 millimeters (mm)
- This means we multiply by 100 when converting dm to mm.
So, 0.003 dm=0.003×100=0.3 mm0.003\ dm = 0.003 \times 100 = 0.3\ mm
Thus, 0.003 decimeters is equal to 0.3 millimeters.
This kind of conversion is vital in technical drawings, mechanical design, and manufacturing, where precision is critical and different units are often used depending on context.
In summary, converting between metric units involves understanding the decimal relationships based on prefixes. Remembering how to shift the decimal point by powers of ten makes these conversions simple and accurate.Answers:
- 450 µg = 0.45 mg
- 0.003 dm = 0.3 mm
Explanation
Understanding unit conversions is a fundamental aspect of science and everyday life, especially when dealing with measurements in fields like medicine, physics, and engineering. Let’s break down both problems to see how the conversions work and why the answers are correct.
1. Converting Micrograms (µg) to Milligrams (mg):
The metric system is based on powers of 10. Here are the relevant prefixes:
- Micro (µ) means one-millionth, or 10−610^{-6}
- Milli (m) means one-thousandth, or 10−310^{-3}
So to convert micrograms to milligrams, we move three decimal places to the left, because a milligram is 1,000 times larger than a microgram. 450 μg=450÷1,000=0.45 mg450\ \mu g = 450 \div 1,000 = 0.45\ mg
Hence, 450 micrograms equals 0.45 milligrams.
This conversion is commonly used in pharmacology. For instance, many drug dosages are prescribed in micrograms but need to be prepared or compared in milligrams.
2. Converting Decimeters (dm) to Millimeters (mm):
Let’s look at the relationships between metric units of length:
- 1 decimeter (dm) = 100 millimeters (mm)
- This means we multiply by 100 when converting dm to mm.
So, 0.003 dm=0.003×100=0.3 mm0.003\ dm = 0.003 \times 100 = 0.3\ mm
Thus, 0.003 decimeters is equal to 0.3 millimeters.
This kind of conversion is vital in technical drawings, mechanical design, and manufacturing, where precision is critical and different units are often used depending on context.
In summary, converting between metric units involves understanding the decimal relationships based on prefixes. Remembering how to shift the decimal point by powers of ten makes these conversions simple and accurate.Answers:
- 450 µg = 0.45 mg
- 0.003 dm = 0.3 mm
Explanation
Understanding unit conversions is a fundamental aspect of science and everyday life, especially when dealing with measurements in fields like medicine, physics, and engineering. Let’s break down both problems to see how the conversions work and why the answers are correct.
1. Converting Micrograms (µg) to Milligrams (mg):
The metric system is based on powers of 10. Here are the relevant prefixes:
- Micro (µ) means one-millionth, or 10−610^{-6}
- Milli (m) means one-thousandth, or 10−310^{-3}
So to convert micrograms to milligrams, we move three decimal places to the left, because a milligram is 1,000 times larger than a microgram. 450 μg=450÷1,000=0.45 mg450\ \mu g = 450 \div 1,000 = 0.45\ mg
Hence, 450 micrograms equals 0.45 milligrams.
This conversion is commonly used in pharmacology. For instance, many drug dosages are prescribed in micrograms but need to be prepared or compared in milligrams.
2. Converting Decimeters (dm) to Millimeters (mm):
Let’s look at the relationships between metric units of length:
- 1 decimeter (dm) = 100 millimeters (mm)
- This means we multiply by 100 when converting dm to mm.
So, 0.003 dm=0.003×100=0.3 mm0.003\ dm = 0.003 \times 100 = 0.3\ mm
Thus, 0.003 decimeters is equal to 0.3 millimeters.
This kind of conversion is vital in technical drawings, mechanical design, and manufacturing, where precision is critical and different units are often used depending on context.
In summary, converting between metric units involves understanding the decimal relationships based on prefixes. Remembering how to shift the decimal point by powers of ten makes these conversions simple and accurate.
