Question

Perform each of the following conversions, being sure to set up 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. \(534.1 \mathrm{~g}\) to pounds f. 1.75 lb to grams g. 8.7 oz to grams h. \(45.9 \mathrm{~g}\) to ounces

Short answer

a. \(0.2543 \mathrm{~kg}\) b. \(2750 \mathrm{~g}\) c. \(6.06271 \mathrm{~lb}\) d. \(96.9977 \mathrm{~oz}\) e. \(1.17751 \mathrm{~lb}\) f. \(793.773 \mathrm{~g}\) g. \(246.440 \mathrm{~g}\) h. \(1.61989 \mathrm{~oz}\)

Step-by-step solution

a. 254.3 g to kilograms

To convert grams to kilograms, divide the given grams by 1000: \(254.3 \mathrm{~g} \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}} = 0.2543 \mathrm{~kg}\)

b. 2.75 kg to grams

To convert kilograms to grams, multiply the given kilograms by 1000: \(2.75 \mathrm{~kg} \times \frac{1000 \mathrm{~g}}{1 \mathrm{~kg}} = 2750 \mathrm{~g}\)

c. 2.75 kg to pounds

To convert kilograms to pounds, use the conversion factor 1 lb = 453.592 g: \(2.75 \mathrm{~kg} \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~kg}} \times \frac{1 \mathrm{~lb}}{453.592 \mathrm{~g}} = 6.06271 \mathrm{~lb}\)

d. 2.75 kg to ounces

To convert kilograms to ounces, use the conversion factor 1 oz = 28.3495 g: \(2.75 \mathrm{~kg} \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~kg}} \times \frac{1 \mathrm{~oz}}{28.3495 \mathrm{~g}} = 96.9977 \mathrm{~oz}\)

e. 534.1 g to pounds

To convert grams to pounds, use the conversion factor 1 lb = 453.592 g: \(534.1 \mathrm{~g} \times \frac{1 \mathrm{~lb}}{453.592 \mathrm{~g}} = 1.17751 \mathrm{~lb}\)

f. 1.75 lb to grams

To convert pounds to grams, use the conversion factor 1 lb = 453.592 g: \(1.75 \mathrm{~lb} \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~lb}} = 793.773 \mathrm{~g}\)

g. 8.7 oz to grams

To convert ounces to grams, use the conversion factor 1 oz = 28.3495 g: \(8.7 \mathrm{~oz} \times \frac{28.3495 \mathrm{~g}}{1 \mathrm{~oz}} = 246.440 \mathrm{~g}\)

h. 45.9 g to ounces

To convert grams to ounces, use the conversion factor 1 oz = 28.3495 g: \(45.9 \mathrm{~g} \times \frac{1 \mathrm{~oz}}{28.3495 \mathrm{~g}} = 1.61989 \mathrm{~oz}\)

Key concepts

Mass Unit Conversion

Understanding mass unit conversion is fundamental in chemistry, as it allows us to express the mass of substances in different units. The process involves using conversion factors, which are ratios that express how many of one unit equals another. By setting up a simple multiplication or division problem, mass can be converted from one unit to another, bridging the gap between different measurement systems.

Converting mass is essential for calculations in lab work, recipe formulation, and even shopping for groceries. Whether it's converting grams to pounds for baking or kilograms to grams for a scientific experiment, knowing how to convert between units accurately is a practical and necessary skill.

Converting Grams to Kilograms

Converting grams (g) to kilograms (kg) is a straightforward process that requires dividing the number of grams by 1,000, since one kilogram is equal to 1,000 grams. For example, if you have 254.3 grams and you want to convert it to kilograms, you would calculate:
254.3 \( \mathrm{g} \) \times \frac{1 \mathrm{~kg}}{1000 \mathrm{~g}} = 0.2543 \mathrm{~kg}

This conversion is particularly useful for scientists working with large quantities of a substance, where measuring in kilograms is more practical than using a large number of grams.

Converting Kilograms to Pounds

Converting kilograms to pounds involves a bit more than our previous conversion, as the units belong to different measurement systems (metric and imperial). One kilogram is approximately equal to 2.20462 pounds. Therefore, the conversion factor commonly used is 1 pound equals 453.592 grams. When converting, for example, 2.75 kilograms into pounds, the calculation would be:
2.75 \( \mathrm{~kg} \) \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~kg}} \times \frac{1 \mathrm{~lb}}{453.592 \mathrm{~g}} = 6.06271 \mathrm{~lb}

Such conversions are essential in daily life, especially when travelling between countries that use different measurement systems, or in international trade of products where mass must be communicated in both metric and imperial units.

Converting Ounces to Grams

To convert ounces (oz) to grams (g), we use the conversion factor that one ounce is equivalent to 28.3495 grams. This conversion is particularly common in cooking and in countries using the imperial system. For instance, converting 8.7 ounces to grams is done as follows:
8.7 \( \mathrm{~oz} \) \times \frac{28.3495 \mathrm{~g}}{1 \mathrm{~oz}} = 246.440 \mathrm{~g}

Understanding this conversion allows for accurate portioning and is critical when following recipes or nutritional guidelines that may present measurements in different units. It's a simple yet essential conversion for bakers, chefs, and anyone involved in food preparation or consumption.