Question

Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor(s) in each case. a. 908 oz to kilograms b. 12.8 L to gallons c. \(125 \mathrm{~mL}\) to quarts d. 2.89 gal to milliliters e. 4.48 lb to grams f. \(550 \mathrm{~mL}\) to quarts

Short answer

a. 908 oz is approximately 25.75 kg. b. 12.8 L is approximately 3.381 gallons. c. 125 mL is approximately 0.132 quarts. d. 2.89 gallons is approximately 10,937 mL. e. 4.48 lb is approximately 2,032 grams. f. 550 mL is approximately 0.581 quarts.

Step-by-step solution

Identify the conversion factor

We need to convert ounces (oz) to kilograms (kg). The conversion factor is: 1 kg = 35.274 oz

Set up the conversion

To do the conversion, we will set up the conversion factor as a fraction such that the original unit (ounces) cancels out and we are left with the desired unit (kilograms): \(908 ~\text{oz} \cdot \dfrac{1 ~\text{kg}}{35.274 ~\text{oz}}\)

Perform the calculation

\(908 ~\text{oz} \cdot \dfrac{1 ~\text{kg}}{35.274 ~\text{oz}} = 25.75 ~\text{kg}\) So, 908 oz is approximately 25.75 kg. #b. 12.8 L to gallons#

Identify the conversion factor

We need to convert liters (L) to gallons (gal). The conversion factor is: 1 gal = 3.78541 L

Set up the conversion

\(12.8 ~\text{L} \cdot \dfrac{1 ~\text{gal}}{3.78541 ~\text{L}}\)

Perform the calculation

\(12.8 ~\text{L} \cdot \dfrac{1 ~\text{gal}}{3.78541 ~\text{L}} = 3.381 ~\text{gal}\) So, 12.8 L is approximately 3.381 gallons. #c. 125 mL to quarts#

Identify the conversion factor

We need to convert milliliters (mL) to quarts (qt). The conversion factor is: 1 qt = 946.353 mL

Set up the conversion

\(125 ~\text{mL} \cdot \dfrac{1 ~\text{qt}}{946.353 ~\text{mL}}\)

Perform the calculation

\(125 ~\text{mL} \cdot \dfrac{1 ~\text{qt}}{946.353 ~\text{mL}} = 0.132 ~\text{qt}\) So, 125 mL is approximately 0.132 quarts. #d. 2.89 gal to milliliters#

Identify the conversion factor

We need to convert gallons (gal) to milliliters (mL). The conversion factor is: 1 gal = 3785.41 mL

Set up the conversion

\(2.89 ~\text{gal} \cdot \dfrac{3785.41 ~\text{mL}}{1 ~\text{gal}}\)

Perform the calculation

\(2.89 ~\text{gal} \cdot \dfrac{3785.41 ~\text{mL}}{1 ~\text{gal}} = 10937 ~\text{mL}\) So, 2.89 gallons is approximately 10,937 mL. #e. 4.48 lb to grams#

Identify the conversion factor

We need to convert pounds (lb) to grams (g). The conversion factor is: 1 lb = 453.592 g

Set up the conversion

\(4.48 ~\text{lb} \cdot \dfrac{453.592 ~\text{g}}{1 ~\text{lb}}\)

Perform the calculation

\(4.48 ~\text{lb} \cdot \dfrac{453.592 ~\text{g}}{1 ~\text{lb}} = 2032 ~\text{g}\) So, 4.48 lb is approximately 2,032 grams. #f. 550 mL to quarts#

Identify the conversion factor

We need to convert milliliters (mL) to quarts (qt). The conversion factor is: 1 qt = 946.353 mL

Set up the conversion

\(550 ~\text{mL} \cdot \dfrac{1 ~\text{qt}}{946.353 ~\text{mL}}\)

Perform the calculation

\(550 ~\text{mL} \cdot \dfrac{1 ~\text{qt}}{946.353 ~\text{mL}} = 0.581 ~\text{qt}\) So, 550 mL is approximately 0.581 quarts.

Key concepts

Conversion Factor

A conversion factor is an essential concept in unit conversion. It is used to transform a quantity expressed in one unit into another unit by multiplying by a fraction that equals one. The fraction is constructed from a known equivalence between two different units.

For example, if you need to convert ounces (oz) to kilograms (kg), the equivalence is:

• 1 kg = 35.274 oz

The conversion factor is chosen to have the original unit in the denominator and the desired unit in the numerator, ensuring that the original unit cancels out. This allows you to focus on the desired units after the calculation.

Utilizing conversion factors effectively is key to mastering conversions in various fields, whether in baking, science, or travel planning.

oz to kg

Converting ounces to kilograms is a common task, especially in contexts involving weight measurements. Let's look at how to perform this conversion effectively.

The conversion factor for converting ounces to kilograms is:

• 1 kg = 35.274 oz

To convert 908 oz to kg, you can set up the conversion as:

• \(908 ~\text{oz} \cdot \dfrac{1 ~\text{kg}}{35.274 ~\text{oz}} = 25.75 ~\text{kg}\)

As shown, the ounces cancel out, and we're left with kilograms. So, 908 ounces is equivalent to approximately 25.75 kilograms. Remember to set up the fraction properly to ensure units cancel out correctly, which is crucial for accurate conversions.

liters to gallons

When converting liters to gallons, the conversion process becomes quite handy for those dealing with large volumes, such as in fluid transport or cooking.

The conversion factor to use here is:

• 1 gallon = 3.78541 liters

Thus, to convert 12.8 liters to gallons:

• \(12.8 ~\text{L} \cdot \dfrac{1 ~\text{gal}}{3.78541 ~\text{L}} = 3.381 ~\text{gal}\)

So, 12.8 liters equals approximately 3.381 gallons. Always ensure the conversion factor is inverted correctly so that liters cancel, leaving the result in gallons. This approach helps you to seamlessly navigate between metric and imperial systems.

mL to quarts

Converting milliliters to quarts is a common requirement in many fields such as medicine, cooking, and science, where precise liquid measurements are crucial.

The conversion factor to use is:

• 1 quart = 946.353 milliliters

For instance, converting 125 milliliters to quarts involves:

• \(125 ~\text{mL} \cdot \dfrac{1 ~\text{qt}}{946.353 ~\text{mL}} = 0.132 ~\text{qt}\)

Here, milliliters cancel out, leaving you with quarts. Therefore, 125 milliliters is approximately 0.132 quarts. This conversion method helps maintain fluidity when performing tasks that require working with both metric and US customary units.