Chapter 2: Problem 66
Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case. a. \(254.3 \mathrm{g}\) to kilograms b. \(2.75 \mathrm{kg}\) to grams c. \(2.75 \mathrm{kg}\) to pounds d. \(2.75 \mathrm{kg}\) to ounces e. \(534.1 \quad \mathrm{g}\) to pounds f. 1.75 lb to grams g. 8.7 oz to grams h. \(45.9 \mathrm{g}\) to ounces
Short Answer
Expert verified
The solutions to the given conversions are as follow:
a. 254.3 g = 0.2543 kg
b. 2.75 kg = 2750 g
c. 2.75 kg = 6.0627 lb
d. 2.75 kg = 96.90314 oz
e. 534.1 g = 1.17751 lb
f. 1.75 lb = 793.78665 g
g. 8.7 oz = 246.64092 g
h. 45.9 g = 1.61808 oz
Step by step solution
01
a. Convert 254.3 g to kilograms
To convert grams to kilograms, we can use the conversion factor: 1 kg = 1000 g.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (kg) on top and the unit we want to convert from (g) at the bottom.
\(Conversion \ factor = \frac{1 \ kg}{1000 \ g}\)
Now, multiply the given mass in grams (254.3 g) by the conversion factor:
\(254.3 \ g \times \frac{1 \ kg}{1000 \ g} \)
The gram (g) unit will cancel between the numerator and denominator:
\(254.3 \times \frac{1 \ kg}{1000}\)
Finally, perform the multiplication:
\(254.3 \times 0.001 \ kg = 0.2543 \ kg\)
The equivalent mass is 0.2543 kg.
02
b. Convert 2.75 kg to grams
To convert kilograms to grams, we use the conversion factor: 1 kg = 1000 g.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (g) on top and the unit we want to convert from (kg) at the bottom.
\(Conversion \ factor = \frac{1000 \ g}{1 \ kg}\)
Now, multiply the given mass in kilograms (2.75 kg) by the conversion factor:
\(2.75 \ kg \times \frac{1000 \ g}{1 \ kg}\)
The kilogram (kg) unit will cancel between the numerator and denominator:
\(2.75 \times \frac{1000 \ g}{1}\)
Finally, perform the multiplication:
\(2.75 \times 1000 \ g = 2750 \ g\)
The equivalent mass is 2750 g.
03
c. Convert 2.75 kg to pounds
To convert kilograms to pounds, we use the conversion factor: 1 kg = 2.20462 lb.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (lb) on top and the unit we want to convert from (kg) at the bottom.
\(Conversion \ factor = \frac{2.20462 \ lb}{1 \ kg}\)
Now, multiply the given mass in kilograms (2.75 kg) by the conversion factor:
\(2.75 \ kg \times \frac{2.20462 \ lb}{1 \ kg}\)
The kilogram (kg) unit will cancel between the numerator and denominator:
\(2.75 \times \frac{2.20462 \ lb}{1}\)
Finally, perform the multiplication:
\(2.75 \times 2.20462 \ lb = 6.0627 \ lb\)
The equivalent mass is 6.0627 lb.
04
d. Convert 2.75 kg to ounces
To convert kilograms to ounces, we use the conversion factor: 1 kg = 35.27396 oz.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (oz) on top and the unit we want to convert from (kg) at the bottom.
\(Conversion \ factor = \frac{35.27396 \ oz}{1 \ kg}\)
Now, multiply the given mass in kilograms (2.75 kg) by the conversion factor:
\(2.75 \ kg \times \frac{35.27396 \ oz}{1 \ kg}\)
The kilogram (kg) unit will cancel between the numerator and denominator:
\(2.75 \times \frac{35.27396 \ oz}{1}\)
Finally, perform the multiplication:
\(2.75 \times 35.27396 \ oz = 96.90314 \ oz\)
The equivalent mass is 96.90314 oz.
05
e. Convert 534.1 g to pounds
To convert grams to pounds, we can use the conversion factor: 1 g = 0.00220462 lb.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (lb) on top and the unit we want to convert from (g) at the bottom.
\(Conversion \ factor = \frac{0.00220462 \ lb}{1 \ g}\)
Now, multiply the given mass in grams (534.1 g) by the conversion factor:
\(534.1 \ g \times \frac{0.00220462 \ lb}{1 \ g}\)
The gram (g) unit will cancel between the numerator and denominator:
\(534.1 \times \frac{0.00220462 \ lb}{1}\)
Finally, perform the multiplication:
\(534.1 \times 0.00220462 \ lb = 1.17751 \ lb\)
The equivalent mass is 1.17751 lb.
06
f. Convert 1.75 lb to grams
To convert pounds to grams, we use the conversion factor: 1 lb = 453.59237 g.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (g) on top and the unit we want to convert from (lb) at the bottom.
\(Conversion \ factor = \frac{453.59237 \ g}{1 \ lb}\)
Now, multiply the given mass in pounds (1.75 lb) by the conversion factor:
\(1.75 \ lb \times \frac{453.59237 \ g}{1 \ lb}\)
The pound (lb) unit will cancel between the numerator and denominator:
\(1.75 \times \frac{453.59237 \ g}{1}\)
Finally, perform the multiplication:
\(1.75 \times 453.59237 \ g = 793.78665 \ g\)
The equivalent mass is 793.78665 g.
07
g. Convert 8.7 oz to grams
To convert ounces to grams, we use the conversion factor: 1 oz = 28.34952 g.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (g) on top and the unit we want to convert from (oz) at the bottom.
\(Conversion \ factor = \frac{28.34952 \ g}{1 \ oz}\)
Now, multiply the given mass in ounces (8.7 oz) by the conversion factor:
\(8.7 \ oz \times \frac{28.34952 \ g}{1 \ oz}\)
The ounce (oz) unit will cancel between the numerator and denominator:
\(8.7 \times \frac{28.34952 \ g}{1}\)
Finally, perform the multiplication:
\(8.7 \times 28.34952 \ g = 246.64092 \ g\)
The equivalent mass is 246.64092 g.
08
h. Convert 45.9 g to ounces
To convert grams to ounces, we use the conversion factor: 1 g = 0.03527396 oz.
To set up the conversion factor, we will write it as a fraction, with the unit we want to convert to (oz) on top and the unit we want to convert from (g) at the bottom.
\(Conversion \ factor = \frac{0.03527396 \ oz}{1 \ g}\)
Now, multiply the given mass in grams (45.9 g) by the conversion factor:
\(45.9 \ g \times \frac{0.03527396 \ oz}{1 \ g}\)
The gram (g) unit will cancel between the numerator and denominator:
\(45.9 \times \frac{0.03527396 \ oz}{1}\)
Finally, perform the multiplication:
\(45.9 \times 0.03527396 \ oz = 1.61808 \ oz\)
The equivalent mass is 1.61808 oz.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Mass Conversion
Mass conversion is an essential concept in chemistry and physics that involves changing the measurement of mass from one unit to another. This is crucial for scientists and students who need to consistently compare measurements and work with different systems of units. Typically, mass conversion involves utilizing a conversion factor—a ratio that expresses how one unit of measure relates to another. An example often used in mass conversion is gram to kilogram, where 1 kilogram equals 1000 grams.
To accurately convert mass, it's important to set up the problem correctly. Start by determining which unit you need to convert to and from, then multiply the original measurement by the appropriate conversion factor to obtain the correct value in the desired units. Understanding this process ensures accurate experimental results and can be applied when scaling recipes in cooking, calculating dosages in medicine, and converting measurements for international standards.
To accurately convert mass, it's important to set up the problem correctly. Start by determining which unit you need to convert to and from, then multiply the original measurement by the appropriate conversion factor to obtain the correct value in the desired units. Understanding this process ensures accurate experimental results and can be applied when scaling recipes in cooking, calculating dosages in medicine, and converting measurements for international standards.
Metric Conversion
Metric conversion refers to the process of converting between different units within the metric system, such as meters to kilometers or grams to milligrams. This system is based on powers of ten, which simplifies the conversion process—often just a matter of moving the decimal point. For instance, to convert millimeters to meters, you divide by 1,000, reflecting the fact that there are 1,000 millimeters in a meter.
The metric system is widely used around the world and is particularly important in scientific research, where consistent and precise measurement is key. Practicing such conversions can help students understand the relative sizes of different units and improve their ability to work with different scales of measurement. Always remember to keep track of the units throughout the conversion to ensure you end with the correct one.
The metric system is widely used around the world and is particularly important in scientific research, where consistent and precise measurement is key. Practicing such conversions can help students understand the relative sizes of different units and improve their ability to work with different scales of measurement. Always remember to keep track of the units throughout the conversion to ensure you end with the correct one.
Weight Conversion
Weight conversion, while often used interchangeably with mass conversion, technically involves the act of changing the measurement of an object's weight (which is influenced by gravity) from one unit to another, such as from pounds to kilograms. In practical terms, when on the Earth's surface, weight is proportional to mass, and the conversion process is similar to that of mass.
The two most common systems for weight conversion are the International System of Units (SI measurements), which uses kilograms, and the Imperial or United States customary system, which uses pounds. To convert between these, one must use the established conversion factor, where 1 kilogram is approximately equal to 2.20462 pounds. Familiarity with these conversions is essential for a wide range of activities from international trade to personal fitness.
The two most common systems for weight conversion are the International System of Units (SI measurements), which uses kilograms, and the Imperial or United States customary system, which uses pounds. To convert between these, one must use the established conversion factor, where 1 kilogram is approximately equal to 2.20462 pounds. Familiarity with these conversions is essential for a wide range of activities from international trade to personal fitness.
Converting Grams to Kilograms
To convert grams to kilograms, understand that the SI unit of mass is the kilogram, and in this system, 1 kilogram is equal to 1,000 grams. Therefore, converting grams to kilograms is a simple process which requires you to divide the number of grams by 1,000.
For example, if you have a mass of 500 grams and you want to express it in kilograms, you would perform the following calculation: \( \frac{500 \text{ g}}{1000} = 0.5 \text{ kg} \). This step is especially relevant in laboratory work or cooking where ingredient measurements may need to be scaled up or down, and accuracy is crucial.
For example, if you have a mass of 500 grams and you want to express it in kilograms, you would perform the following calculation: \( \frac{500 \text{ g}}{1000} = 0.5 \text{ kg} \). This step is especially relevant in laboratory work or cooking where ingredient measurements may need to be scaled up or down, and accuracy is crucial.
Converting Kilograms to Grams
When converting kilograms to grams, you are essentially converting from a larger unit to a smaller unit within the metric system. Since 1 kilogram is 1,000 grams, the process involves multiplying the number of kilograms by 1,000.
Taking an example, converting 2 kilograms to grams would involve the calculation \( 2 \text{ kg} \times 1000 = 2000 \text{ g} \). This is a frequent calculation in various scenarios, from packaging of goods, where weight needs to be listed in grams (or kilograms), to scientific experiments requiring precise measurements in smaller units.
Taking an example, converting 2 kilograms to grams would involve the calculation \( 2 \text{ kg} \times 1000 = 2000 \text{ g} \). This is a frequent calculation in various scenarios, from packaging of goods, where weight needs to be listed in grams (or kilograms), to scientific experiments requiring precise measurements in smaller units.
Converting Kilograms to Pounds
The conversion of kilograms to pounds is a common task, especially when dealing with international trade, travel, recipes, and many scientific applications. A pound is an Imperial unit of mass, and to convert kilograms to pounds, one uses the conversion factor 1 kilogram is equivalent to approximately 2.20462 pounds.
To convert, multiply the mass value in kilograms by the conversion factor: \( \text{mass in kg} \times 2.20462 = \text{mass in lb} \). For example, to convert 5 kilograms to pounds, calculate \( 5 \text{ kg} \times 2.20462 = 11.0231 \text{ lb} \). This conversion is useful when you are working with equipment that only measures in pounds, such as in fitness centers or when using certain weighing scales.
To convert, multiply the mass value in kilograms by the conversion factor: \( \text{mass in kg} \times 2.20462 = \text{mass in lb} \). For example, to convert 5 kilograms to pounds, calculate \( 5 \text{ kg} \times 2.20462 = 11.0231 \text{ lb} \). This conversion is useful when you are working with equipment that only measures in pounds, such as in fitness centers or when using certain weighing scales.
Converting Grams to Ounces
Grams to ounces conversion is another frequently encountered task, especially in contexts involving food recipes and postal services. The ounce is an Imperial unit of mass, and to convert grams to ounces, one uses the conversion factor that 1 gram is approximately equal to 0.03527396 ounces.
Thus, you multiply the number of grams by this conversion factor to get the equivalent in ounces: \( \text{mass in g} \times 0.03527396 = \text{mass in oz} \). For example, a chocolate bar weighing 100 grams can be converted to ounces by calculating \( 100 \text{ g} \times 0.03527396 = 3.527396 \text{ oz} \). This conversion comes in handy when dealing with shipping goods internationally, as shipping rates are often based on weight, historically in pounds and ounces.
Thus, you multiply the number of grams by this conversion factor to get the equivalent in ounces: \( \text{mass in g} \times 0.03527396 = \text{mass in oz} \). For example, a chocolate bar weighing 100 grams can be converted to ounces by calculating \( 100 \text{ g} \times 0.03527396 = 3.527396 \text{ oz} \). This conversion comes in handy when dealing with shipping goods internationally, as shipping rates are often based on weight, historically in pounds and ounces.
