Converting between different units of measurement is an essential skill in many scientific, engineering, and industrial fields. One such conversion involves converting grain per gallon (gr/gal) to gram per cubic millimeter (g/mm³). This guide will walk you through the step-by-step process of converting 154.6 grain per gallon into gram per cubic millimeter, breaking down the units and applying the necessary conversion factors.
Understanding the Units
Before we perform the conversion, let’s first understand the units involved:
1. Grain per Gallon (gr/gal)
- The grain (gr) is a unit of mass commonly used in measuring small quantities, particularly in ammunition, pharmaceuticals, and water hardness.
- The gallon (gal) is a unit of volume that varies depending on the measurement system. In this guide, we will use the U.S. gallon, which is widely used in the United States.
2. Gram per Cubic Millimeter (g/mm³)
- The gram (g) is a standard metric unit of mass.
- The cubic millimeter (mm³) is a metric unit of volume, equal to 1×10−91 \times 10^{-9}1×10−9 cubic meters.
To perform the conversion, we need to know the relationships between these units.
Step-by-Step Conversion Process
Step 1: Convert Grain to Grams
One grain is defined as:1 grain=0.06479891 grams1 \text{ grain} = 0.06479891 \text{ grams}1 grain=0.06479891 grams
Therefore, converting 154.6 grains to grams:154.6×0.06479891=10.0259 grams154.6 \times 0.06479891 = 10.0259 \text{ grams}154.6×0.06479891=10.0259 grams
Step 2: Convert Gallon to Cubic Millimeters
We use the U.S. gallon, which is equal to 3,785,411.784 cubic millimeters (mm³):1 gallon=3,785,411.784 mm31 \text{ gallon} = 3,785,411.784 \text{ mm}^31 gallon=3,785,411.784 mm3
Now, let’s divide the mass (grams) by the volume (cubic millimeters) to find the concentration in g/mm³:10.0259 g3,785,411.784 mm3\frac{10.0259 \text{ g}}{3,785,411.784 \text{ mm}^3}3,785,411.784 mm310.0259 g
Performing the division:10.0259÷3,785,411.784=2.65×10−6 g/mm310.0259 \div 3,785,411.784 = 2.65 \times 10^{-6} \text{ g/mm}^310.0259÷3,785,411.784=2.65×10−6 g/mm3
Final Answer
Thus, 154.6 grain per gallon is approximately:2.65×10−6 g/mm32.65 \times 10^{-6} \text{ g/mm}^32.65×10−6 g/mm3
or in decimal form:0.00000265 g/mm30.00000265 \text{ g/mm}^30.00000265 g/mm3
Why Is This Conversion Useful?
This conversion is commonly used in various scientific and industrial applications, including:
- Water Treatment: Measuring impurities and hardness in water.
- Pharmaceuticals: Determining precise drug concentrations.
- Metallurgy: Analyzing material densities and compositions.
By understanding and applying these unit conversions, you can ensure accurate measurements in your respective field.