Question

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

Short answer

a. \(25.763\, \mathrm{kg}\) b. \(3.381\, \mathrm{gal}\) c. \(0.132\, \mathrm{qt}\) d. \(10939.33\, \mathrm{mL}\) e. \(2032.12\, \mathrm{g}\) f. \(0.581\, \mathrm{qt}\)

Step-by-step solution

a. Conversion factor for oz to kg

The conversion factor we need is 1 oz = 0.0283495 kg. We'll multiply the value we have in oz (908 oz) by the conversion factor to get the value in kg.

a. Calculate the value in kg

Using the conversion factor, we can calculate the value in kilograms: \(908\, \mathrm{oz} \times 0.0283495\, \frac{\mathrm{kg}}{\mathrm{oz}} = 25.763\, \mathrm{kg}\) b. Convert 12.8 L to gallons

b. Conversion factor for L to gal

The conversion factor we need is 1 L = 0.264172 gal. We'll multiply the value we have in liters (12.8 L) by the conversion factor to get the value in gallons.

b. Calculate the value in gal

Using the conversion factor, we can calculate the value in gallons: \(12.8\, \mathrm{L} \times 0.264172\, \frac{\mathrm{gal}}{\mathrm{L}} = 3.381\, \mathrm{gal}\) c. Convert 125 mL to quarts

c. Conversion factor for mL to qt

The conversion factor we need is 1 mL = 0.001057 qt. We'll multiply the value we have in milliliters (125 mL) by the conversion factor to get the value in quarts.

c. Calculate the value in qt

Using the conversion factor, we can calculate the value in quarts: \(125\, \mathrm{mL} \times 0.001057\, \frac{\mathrm{qt}}{\mathrm{mL}} = 0.132\, \mathrm{qt}\) d. Convert 2.89 gal to milliliters

d. Conversion factor for gal to mL

The conversion factor we need is 1 gal = 3785.41 mL. We'll multiply the value we have in gallons (2.89 gal) by the conversion factor to get the value in milliliters.

d. Calculate the value in mL

Using the conversion factor, we can calculate the value in milliliters: \(2.89\, \mathrm{gal} \times 3785.41\, \frac{\mathrm{mL}}{\mathrm{gal}} = 10939.33\, \mathrm{mL}\) e. Convert 4.48 lb to grams

e. Conversion factor for lb to g

The conversion factor we need is 1 lb = 453.592 g. We'll multiply the value we have in pounds (4.48 lb) by the conversion factor to get the value in grams.

e. Calculate the value in g

Using the conversion factor, we can calculate the value in grams: \(4.48\, \mathrm{lb} \times 453.592\, \frac{\mathrm{g}}{\mathrm{lb}} = 2032.12\, \mathrm{g}\) f. Convert 550 mL to quarts

f. Conversion factor for mL to qt

The conversion factor we need is 1 mL = 0.001057 qt. We'll multiply the value we have in milliliters (550 mL) by the conversion factor to get the value in quarts.

f. Calculate the value in qt

Using the conversion factor, we can calculate the value in quarts: \(550\, \mathrm{mL} \times 0.001057\, \frac{\mathrm{qt}}{\mathrm{mL}} = 0.581\, \mathrm{qt}\)

Key concepts

Conversion Factors

Conversion factors are numerical values used to change a quantity expressed in one unit into an equivalent quantity expressed in another unit. They act like a bridge between two different measurement systems or units within the same system. A conversion factor is derived from the equivalence of two units and is dimensionless, which means its value is 1. For example, the conversion factor from ounces (oz) to kilograms (kg) is 0.0283495 because 1 oz is equal to 0.0283495 kg. To convert, multiply the original value by the conversion factor.

• 1 oz = 0.0283495 kg
• 1 L = 0.264172 gal
• 1 mL = 0.001057 qt

These conversion factors make it easy to switch between units by simple multiplication. Always double-check which units are involved and use the appropriate conversion factor for accurate conversions.

Metric System

The metric system is an international decimal-based system of measurement used by most countries in the world. It's designed to be simple and universal. Units in the metric system are based on powers of 10, making it easier to convert within the system.
Units of measurement in the metric system include the meter (m) for length, the liter (L) for volume, and the gram (g) for mass. To convert between metric units, you simply multiply or divide by powers of 10. For example, 1000 milliliters (mL) is equivalent to 1 liter (L).

• Length: millimeter (mm), centimeter (cm), meter (m)
• Mass: milligram (mg), gram (g), kilogram (kg)
• Volume: milliliter (mL), liter (L)

Because it is used worldwide, it simplifies scientific calculations and communications.

Imperial System

The imperial system of measurement was historically used in the United Kingdom and is still predominantly used in the United States. Unlike the metric system, the imperial system is not based on powers of ten, making conversions within the system less intuitive.
It includes units like inches, feet, and miles for length; pounds (lb) and ounces (oz) for mass; and gallons and quarts for volume. Because conversion factors are not standardized around base ten, converting between units can be challenging.

• Length: inch, foot, yard, mile
• Mass: ounce, pound
• Volume: teaspoon, tablespoon, fluid ounce, cup, pint, quart, gallon

Understanding the conversions between the imperial system and other measurement systems is important, especially for travel or when using resources from the U.S.

Mass Conversion

Mass conversion involves changing a mass value from one unit of measurement to another. This is often necessary in science, medicine, cooking, and many other fields. For example, converting pounds (lb) to grams (g) is common in recipes and nutritional information.
One pound (lb) equals 453.592 grams (g). To convert pounds to grams, multiply the number of pounds by the conversion factor 453.592.

• 4.48 lb = 4.48 × 453.592 g = 2032.12 g

For ounces to kilograms, use the conversion factor where 1 oz is equal to 0.0283495 kg. Multiply the number of ounces by this conversion factor to get the equivalent weight in kilograms.
Mass conversions are essential for ensuring that measurements are accurate and that products meet specified standards.

Volume Conversion

Volume conversion is the process of converting between different volume units, such as liters to gallons or milliliters to quarts. Understanding these conversions is important for various real-life situations, like cooking, fuel measurement, and scientific experiments.
For instance, when converting liters (L) to gallons (gal), use the conversion factor where 1 L is equal to 0.264172 gal. Multiply the number of liters by this conversion factor.

• 12.8 L = 12.8 × 0.264172 gal = 3.381 gal

Similarly, to convert milliliters (mL) to quarts (qt), use the conversion factor 1 mL equals 0.001057 qt.

• 125 mL = 125 × 0.001057 qt = 0.132 qt

Volume conversions ensure that liquid or space measures are exact, critical for scientific integrity and everyday life applications.