Question

Express the density of water in the English units of pounds per gallon.

Short answer

The density of water in English units is approximately 8.34 lbs/gallon.

Step-by-step solution

Understand the Known Values and Units

We know that the density of water is commonly defined in metric units as approximately 1 gram per cubic centimeter (g/cm³). To convert this into English units, we need to understand this in terms of pounds per gallon.

Conversion from Grams to Pounds

First, we need to convert grams to pounds. We know that 1 pound is equal to approximately 453.592 grams. Thus, we have the relationship:\[1 \text{ pound} = 453.592 \text{ grams}\]This means that 1 gram is equal to\[\frac{1}{453.592} \text{ pounds}\]or approximately 0.00220462 pounds.

Conversion from Cubic Centimeters to Gallons

Next, convert cubic centimeters to gallons. We know that 1 gallon is equivalent to 231 cubic inches. Since 1 inch is equivalent to 2.54 centimeters, we find:\[1 \text{ inch} = 2.54 \text{ cm} \]Therefore,\[1 \text{ cubic inch} = (2.54)^3 \text{ cm}^3 = 16.387064 \text{ cm}^3\]Thus, 1 gallon is equivalent to\[16.387064 \, \text{cm}^3 / \text{inch}^3 \times 231 \, \text{inch}^3 / \text{gallon} \]which is approximately 3785.41 cm³.

Calculate Density in Pounds per Gallon

After converting the volume, we can now calculate density in pounds per gallon:Given that water has a density of 1 g/cm³:\[1 \, \text{g/cm}^3 = 0.00220462 \, \text{lb/cm}^3\]And knowing 1 gallon = 3785.41 cm³:\[\text{Density in lb/gallon} = 0.00220462 \ imes 3785.41 \]Calculating this gives us approximately 8.34 lbs/gallon.

Key concepts

Conversion of Units

Conversion of units involves changing a measurement from one unit to another. This is an essential skill in many fields like science and engineering. The process of unit conversion relies on understanding the relationship between different units. In this particular exercise, we are converting density from metric units (\(g/cm^3\)) to English units (\(lb/gallon\)).

To perform a conversion, you need a conversion factor, which is a ratio expressing how many of one unit equals another. For example, to convert grams to pounds, we use the factor that 1 pound is approximately equal to 453.592 grams.

Similarly, when converting cubic centimeters to gallons, we utilize the fact that 1 gallon is equivalent to 3785.41 cubic centimeters. When doing these conversions, it's useful to write out each step. This includes setting up the conversion factors so units cancel out appropriately, leading to your desired unit.

English Units

Understanding English units is particularly important in contexts where the imperial system is traditionally used. Unlike the metric system, which is based on decimalization, the English or imperial system uses more varied conversion factors. For instance:

• A pound is the basic unit of mass in the English system.
• A gallon is the standard unit for liquid volume.

To fully grasp English units, it's beneficial to be familiar with common conversions, like:

• 1 inch = 2.54 centimeters, necessary for volume conversions.
• 1 pound = 453.592 grams, crucial for mass conversions.

These measurements are valuable when expressing scientific properties, like density, in English units, which can differ from the universally applicable metric system.

Metric to English Conversion

Converting from metric to English units is an everyday necessity in scenarios where different systems are in use. This process involves understanding both systems and how they relate. In this exercise, you’re converting water's density from metric units, specifically \(g/cm^3\), to English units, \(lb/gallon\).

The steps include converting the individual components of density: grams to pounds, and cubic centimeters to gallons. Knowing these essential conversion factors is crucial:

• 1 gram = 0.00220462 pounds.
• 1 cubic centimeter = 1/3785.41 gallon.

By multiplying these conversions, you transform the density value across systems. This allows you to communicate findings or use measurements in contexts where English units are standard, while maintaining accuracy and consistent understanding between the two systems.