Convert grams per deciliter to milligrams per liter

Convert grams per deciliter to milligrams per liter. Select the correct units and conversion factors for each step in the following unit roadmap Unit roadmap: g dL mg dL Conversion factors and units: 19 10L 1 dl mg L L mg 10 L 1L 1000 mg 1L X X 1 mg 1000 g X 1000 g 1 mg 1000 mg 1g 1dL 10L 10 L

The Correct Answer and Explanation is :

To convert grams per deciliter (g/dL) to milligrams per liter (mg/L), we need to carefully follow the unit conversion roadmap provided in your question. The steps involve a series of conversions between units of mass, volume, and concentration. Let’s break down the process:

Step-by-Step Conversion Process:

1. Starting Units: We begin with grams per deciliter (g/dL).
2. Convert Grams to Milligrams:

• 1 gram (g) = 1000 milligrams (mg).
• So, 1 g = 1000 mg. Therefore, to convert grams to milligrams, multiply by 1000.

1. Convert Deciliters to Liters:

• 1 deciliter (dL) = 0.1 liter (L), or equivalently, 1 dL = 10^-1 L.
• To convert from deciliters to liters, you divide by 10, or multiply by 0.1.

1. Combine the Conversions:
   We need to convert g/dL to mg/L. Start by converting the mass (g to mg) and then the volume (dL to L): [
   \text{grams per deciliter (g/dL)} \rightarrow \text{grams to milligrams} \rightarrow \text{milligrams per deciliter}
   ]
   [
   \text{milligrams per deciliter} \rightarrow \text{deciliters to liters} \rightarrow \text{milligrams per liter (mg/L)}
   ]

Mathematical Conversion:

1. Start with 1 g/dL:
   [
   1 \, \text{g/dL} \times \frac{1000 \, \text{mg}}{1 \, \text{g}} = 1000 \, \text{mg/dL}
   ]
2. Convert mg/dL to mg/L:
   [
   1000 \, \text{mg/dL} \times \frac{10 \, \text{dL}}{1 \, \text{L}} = 10,000 \, \text{mg/L}
   ]

Final Answer:

So, 1 g/dL = 10,000 mg/L.

Explanation:

• Why grams to milligrams? Grams are a larger unit than milligrams, so to increase the quantity, we multiply by 1000. This conversion is common in metric systems for converting between larger and smaller units of mass.
• Why deciliters to liters? Deciliters are a smaller unit of volume compared to liters. Since 1 dL = 0.1 L (or 1/10 L), we convert by multiplying the deciliter value by 10 to get the volume in liters.

This unit conversion process ensures that we account for both mass and volume adjustments when converting concentration from g/dL to mg/L. The final result is that 1 gram per deciliter (g/dL) is equivalent to 10,000 milligrams per liter (mg/L).