Question

Perform the following unit conversions. a. 908 oz to kilograms b. \(12.8 \mathrm{~L}\) to gallons c. \(125 \mathrm{~mL}\) to quarts d. \(2.89\) gal to milliliters e. \(4.48 \mathrm{lb}\) to grams f. \(550 \mathrm{~mL}\) to quarts

Short answer

a. 25.754 kg b. 3.3817 gal c. 0.13197 qt d. 10931.49 mL e. 2032.123 g f. 0.5812 qt

Step-by-step solution

a. 908 oz to kilograms

1. Identify the conversion factor: \[1 \mathrm{~kg} = 35.274 \mathrm{~oz}\] 2. Multiply the given value by the conversion factor: \(\frac{908 \mathrm{~oz}}{1} \times \frac{1 \mathrm{~kg}}{35.274 \mathrm{~oz}}\) 3. Calculate the result: \(908 \mathrm{~oz} \times \frac{1 \mathrm{~kg}}{35.274 \mathrm{~oz}} = 25.754 \mathrm{~kg}\)

b. 12.8 L to gallons

1. Identify the conversion factor: \[1 \mathrm{~gal} = 3.78541 \mathrm{~L}\] 2. Multiply the given value by the conversion factor: \(\frac{12.8 \mathrm{~L}}{1} \times \frac{1 \mathrm{~gal}}{3.78541 \mathrm{~L}}\) 3. Calculate the result: \(12.8 \mathrm{~L} \times \frac{1 \mathrm{~gal}}{3.78541 \mathrm{~L}} = 3.3817 \mathrm{~gal}\)

c. 125 mL to quarts

1. Identify the conversion factor: \[1 \mathrm{~qt} = 946.353 \mathrm{~mL}\] 2. Multiply the given value by the conversion factor: \(\frac{125 \mathrm{~mL}}{1} \times \frac{1 \mathrm{~qt}}{946.353 \mathrm{~mL}}\) 3. Calculate the result: \(125 \mathrm{~mL} \times \frac{1 \mathrm{~qt}}{946.353 \mathrm{~mL}} = 0.13197 \mathrm{~qt}\)

d. 2.89 gal to milliliters

1. Identify the conversion factor: \[1 \mathrm{~gal} = 3785.41 \mathrm{~mL}\] 2. Multiply the given value by the conversion factor: \(\frac{2.89 \mathrm{~gal}}{1} \times \frac{3785.41 \mathrm{~mL}}{1 \mathrm{~gal}}\) 3. Calculate the result: \(2.89 \mathrm{~gal} \times \frac{3785.41 \mathrm{~mL}}{1 \mathrm{~gal}} = 10931.49 \mathrm{~mL}\)

e. 4.48 lb to grams

1. Identify the conversion factor: \[1 \mathrm{~lb} = 453.592 \mathrm{~g}\] 2. Multiply the given value by the conversion factor: \(\frac{4.48 \mathrm{~lb}}{1} \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~lb}}\) 3. Calculate the result: \(4.48 \mathrm{~lb} \times \frac{453.592 \mathrm{~g}}{1 \mathrm{~lb}} = 2032.123 \mathrm{~g}\)

f. 550 mL to quarts

1. Identify the conversion factor: \[1 \mathrm{~qt} = 946.353 \mathrm{~mL}\] 2. Multiply the given value by the conversion factor: \(\frac{550 \mathrm{~mL}}{1} \times \frac{1 \mathrm{~qt}}{946.353 \mathrm{~mL}}\) 3. Calculate the result: \(550 \mathrm{~mL} \times \frac{1 \mathrm{~qt}}{946.353 \mathrm{~mL}} = 0.5812 \mathrm{~qt}\)

Key concepts

Conversion Factors

Conversion factors are crucial for switching between different units of measurement. Think of them as the bridge that allows you to translate one set of measurements into another. It's like having a bilingual dictionary for numbers. To convert units, you multiply the given value by an appropriate conversion factor that represents the relationship between the two units.

For example, if we want to convert ounces to kilograms, we use the conversion factor where 1 kilogram equals approximately 35.274 ounces. Likewise, converting liters to gallons involves the conversion factor that 1 gallon is about 3.78541 liters. The beautiful part about conversion factors is that they simplify the process of unit conversion to basic multiplication and division.

Remember that conversion factors can originate from both the metric and imperial systems, facilitating transitions between them. Always make sure to use the correct conversion factor for an accurate conversion.

Measurement Units

Measurement units are fundamental to quantifying and communicating quantities clearly. They allow us to describe dimensions such as length, mass, volume, and temperature. Understanding measurement units is like learning the alphabet of the science world.

Each unit belongs to a specific category, such as:

• Length: meters, feet
• Mass: grams, pounds
• Volume: liters, gallons

Comprehensively knowing these units paves the way for proficiently handling mathematical calculations involving everyday topics like cooking, building, and scientific research. Correctly reading and interpreting these units ensures precision and effectiveness in any field.

Metric System

The metric system is an international decimalized system of measurement that is used globally. It is based on powers of ten, which makes it especially easy to convert between different scales. This system includes units like the meter for length, the kilogram for mass, and the liter for volume.

The simplicity of the metric system is one of its greatest strengths. To convert within the metric system, you typically just move the decimal point. For example, converting 1000 milliliters to liters is as simple as shifting the decimal three places to get 1 liter. Such straightforward conversions are why the metric system is the preferred measurement system in scientific communities.

Mastering the metric system opens up a world of consistency and simplification, aligning with most global standards of measurement.

Imperial System

The imperial system is widely used in certain countries, notably the United States and historically in the British Empire, which explains its name. It includes units such as inches for length, pounds for mass, and gallons for volume.

Unlike the metric system, the imperial system does not rely on a uniform base ten structure. This can make conversions a bit trickier, as you often need specific conversion factors, such as 1 gallon being equivalent to 3.78541 liters, to perform accurate conversions.

Despite these challenges, understanding the imperial system is valuable, especially in contexts where these units are prevalent, like when dealing with certain American or British recipes, measurements, or industries. The key is using accurate conversion factors to transition smoothly between imperial and metric systems.