The white blood cell concentration in normal blood is approximately 12,000 cells/mm³ of blood. How many white blood cells does a normal adult with 5 L of blood have? Express the answer in scientific notation.

Verified step by step guidance

1. Step 1: Start by identifying the given information. The white blood cell concentration is 12,000 cells/mm², and the total blood volume is 5 L. Note that we need to convert the blood volume from liters to cubic millimeters (mm³) since the concentration is given in cells per mm².
2. Step 2: Use the conversion factor for volume: 1 L = 1,000 mL and 1 mL = 1,000 mm³. Therefore, 1 L = 1,000,000 mm³. Multiply the given blood volume (5 L) by this conversion factor to find the total blood volume in mm³.
3. Step 3: Recognize that the concentration is given in cells per mm², but we need to express the total number of cells. Assume the blood is evenly distributed in a 1 mm thickness layer, so the concentration in cells/mm² is equivalent to cells/mm³. This allows us to directly multiply the concentration by the total blood volume in mm³.
4. Step 4: Multiply the white blood cell concentration (12,000 cells/mm³) by the total blood volume in mm³ (calculated in Step 2). This will give the total number of white blood cells in the blood.
5. Step 5: Express the result in scientific notation by adjusting the decimal point and using the appropriate power of 10. Ensure the final answer is formatted correctly as required.

Key Concepts

White Blood Cell Concentration

White blood cell concentration refers to the number of white blood cells (WBCs) present in a specific volume of blood, typically measured in cells per cubic millimeter (cells/mm^3). In normal adults, this concentration is approximately 12,000 cells/mm^3, which is crucial for understanding immune function and diagnosing various health conditions.

Volume of Blood

The volume of blood in an adult human is generally around 5 liters. This total blood volume is important for calculating the total number of cells in the bloodstream, as it provides the necessary context for converting concentration measurements into absolute quantities of cells.

Scientific Notation

Scientific notation is a method of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically formatted as a number between 1 and 10 multiplied by a power of ten (e.g., 1.2 x 10^4). This notation simplifies calculations and comparisons, especially in scientific contexts.