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Mobile App Chapter 2: Problem 19
Complete the following metric conversions using the correct number of significant figures: (a) \(28.0 \mathrm{~cm}\) to \(\mathrm{m}\) (b) \(1000 \mathrm{~m}\) to \(\mathrm{km}\) (c) \(9.28 \mathrm{~cm}\) to \(\mathrm{mm}\) (d) \(10.68 \mathrm{~g}\) to \(\mathrm{mg}\) (e) \(6.8 \times 10^{4} \mathrm{mg}\) to \(\mathrm{kg}\) (f) \(8.54 \mathrm{~g}\) to \(\mathrm{kg}\) (g) \(25.0 \mathrm{~mL}\) to \(\mathrm{L}\) (h) \(22.4 \mathrm{~L}\) to \(\mu \mathrm{L}\)
Short Answer
Expert verified
a) 0.280 m; b) 1.0 km; c) 92.8 mm; d) 10680 mg; e) 6.8×10^-2 kg; f) 0.00854 kg; g) 0.0250 L; h) 22400000 µL
Step by step solution
01
Convert \(28.0 \, \text{cm}\) to \(\text{m}\)
1 meter (m) = 100 centimeters (cm). To convert from cm to m, divide by 100. \(28.0 \, \text{cm} \div 100 = 0.280 \, \text{m}\). Since the original number has 3 significant figures, the answer should also have 3 significant figures.
02
Convert \(1000 \, \text{m}\) to \(\text{km}\)
1 kilometer (km) = 1000 meters (m). To convert from m to km, divide by 1000. \(1000 \, \text{m} \div 1000 = 1.0 \, \text{km}\). Since the original number has 4 significant figures, the answer should also have 4 significant figures.
03
Convert \(9.28 \, \text{cm}\) to \(\text{mm}\)
1 centimeter (cm) = 10 millimeters (mm). To convert from cm to mm, multiply by 10. \(9.28 \, \text{cm} \times 10 = 92.8 \, \text{mm}\). Since the original number has 3 significant figures, the answer should also have 3 significant figures.
04
Convert \(10.68 \, \text{g}\) to \(\text{mg}\)
1 gram (g) = 1000 milligrams (mg). To convert from g to mg, multiply by 1000. \(10.68 \, \text{g} \times 1000 = 10680 \, \text{mg}\). Since the original number has 4 significant figures, the answer should also have 4 significant figures.
05
Convert \(6.8 \times 10^4 \, \text{mg}\) to \(\text{kg}\)
1 kilogram (kg) = 1,000,000 milligrams (mg). To convert from mg to kg, divide by 1,000,000. \(6.8 \times 10^4 \, \text{mg} \div 1,000,000 = 6.8 \times 10^{-2} \, \text{kg}\). Since the original number has 2 significant figures, the answer should also have 2 significant figures.
06
Convert \(8.54 \, \text{g}\) to \(\text{kg}\)
1 kilogram (kg) = 1000 grams (g). To convert from g to kg, divide by 1000. \(8.54 \, \text{g} \div 1000 = 0.00854 \, \text{kg}\). Since the original number has 3 significant figures, the answer should also have 3 significant figures.
07
Convert \(25.0 \, \text{mL}\) to \(\text{L}\)
1 liter (L) = 1000 milliliters (mL). To convert from mL to L, divide by 1000. \(25.0 \, \text{mL} \div 1000 = 0.0250 \, \text{L}\). Since the original number has 3 significant figures, the answer should also have 3 significant figures.
08
Convert \(22.4 \, \text{L}\) to \(\mu \text{L}\)
1 liter (L) = 1,000,000 microliters (µL). To convert from L to µL, multiply by 1,000,000. \(22.4 \, \text{L} \times 1,000,000 = 22,400,000 \, \mu \text{L}\). Since the original number has 3 significant figures, the answer should also have 3 significant figures.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
significant figures
Significant figures are essential in chemistry and many other sciences because they tell us about the precision of a measurement. When performing metric conversions, it's crucial to maintain the correct number of significant figures for accuracy. For instance, if you start with 3 significant figures in centimeters, your converted value in meters should also have 3 significant figures.
Here's a quick guideline on identifying significant figures:
Here's a quick guideline on identifying significant figures:
- All non-zero digits are significant.
- Any zeros between significant digits are also significant.
- Leading zeros (zeros to the left of the first non-zero digit) are not significant.
- Trailing zeros in a decimal number are significant.
metric system
The metric system is a universal decimal-based system of measurement, used widely across the world, especially in science and engineering. It's crucial to understand and be comfortable with the basic units and their conversions.
Here are some core metric units and their common conversions:
Here are some core metric units and their common conversions:
- Length: meter (m), centimeters (cm), millimeters (mm), kilometers (km)
- Mass: gram (g), milligrams (mg), kilograms (kg)
- Volume: liter (L), milliliters (mL), microliters (µL)
unit conversions
Unit conversions are a fundamental aspect of working within the metric system. The key is to understand the relationship between different units and to apply them correctly.
Here's a breakdown of the process using steps:
\[ 28.0 \, \text{cm} \div 100 = 0.280 \, \text{m} \] This ensures the conversion is done correctly while maintaining precision.
Here's a breakdown of the process using steps:
- Identify the units you are converting from and to.
- Determine the conversion factor between these units. For example, 1 meter = 100 centimeters.
- If converting to a larger unit, divide by the conversion factor. If converting to a smaller unit, multiply by the conversion factor.
- Ensure your final answer has the correct number of significant figures.
\[ 28.0 \, \text{cm} \div 100 = 0.280 \, \text{m} \] This ensures the conversion is done correctly while maintaining precision.
dimensional analysis
Dimensional analysis, also known as the factor-label method or unit factor method, is a technique used to convert units from one measurement system to another. This method helps ensure that the final units are correct and that all conversions are appropriately done.
Steps for dimensional analysis:
\[ 22.4 \, \text{L} \times \frac {1,000,000 \, \mu \text{L}}{1 \, \text{L}} = 22,400,000 \, \mu \text{L} \] This method ensures accuracy and clarity in unit conversions, maintaining the integrity of measurements.
Steps for dimensional analysis:
- Write down the quantity you are starting with.
- Set up the conversion factor so that the unwanted unit cancels out, leaving only the desired unit.
- Multiply through by the conversion factor.
- Make sure the units cancel out appropriately and that your final answer has the correct unit.
\[ 22.4 \, \text{L} \times \frac {1,000,000 \, \mu \text{L}}{1 \, \text{L}} = 22,400,000 \, \mu \text{L} \] This method ensures accuracy and clarity in unit conversions, maintaining the integrity of measurements.
