Start by finding how many cubic millimeters there are in 500 milliliters of blood.
B
Multiply the number of cubic millimeters in the donation by the number of red blood cells per cubic millimeter.
C
Powers with the same base have greater values when they have greater exponents.
A
5 * 10^9
B
25 * 10^(11)
C
The number of red blood cells in a sample donation is greater than the number of white blood cells.
Practice makes perfect
A sample blood donation is 500 milliliters. One cubic millimeter of blood contains about 10^4 white blood cells. We want to find the number of white blood cells in the donation. Let's start by rewriting the volume of the donation into cubic millimeters.
1 mm^3 = 10^(- 3) mL
In other words, we want to find how many cubic millimeters there are in 500 milliliters. To do this, we can calculate their ratio. It divides the donation into parts with the volume of one cubic millimeter.
500 mL/1 mm^3 = 500 mL/10^(- 3) mL
The result is the number of cubic millimeters in 500 milliliters. Notice that the unit of milliliters is a factor that can be reduced.
We found the number of cubic millimeters in the blood donation. Now, each cubic millimeter of blood contains about 10^4 white blood cells. We will multiply the number of cubic millimeters by the number of white blood cells per cubic millimeter to find the approximate number of white blood cells in the donation.
5 * 10^5 * 10^4
We will use the Product of Powers Property to simplify this product.
There are approximately 5 * 10^9 white blood cells in the donation.
Now, we want to find the approximate number of red blood cells in the donation knowing that one cubic millimeter of blood contains about 5 * 10^6 red blood cells. We will use the number of cubic millimeters in the blood donation we found in Part A.
5 * 10^5
We will multiply the number of cubic millimeters by the number of red blood cells per cubic millimeter to calculate the approximate number of red blood cells in the donation.
5 * 10^5 * 5 * 10^6
Finally, we will again use the Product of Powers Property to simplify this product.
There are approximately 25 * 10^(11) red blood cells in the donation.
We want to compare the answers found in Part A and in Part B, which means that we want to know which number is greater. In other words, we want to determine if the blood donation contains more white blood cells or more red blood cells. Let's recall the numbers from previous parts!
Number of White Blood Cells
Number of Red Blood Cells
5 * 10^9
25 * 10^(11)
Let's rewrite all factors as powers so that it will be easier to compare the expressions.
Number of White Blood Cells
Number of Red Blood Cells
5^1 * 10^9
5^2 * 10^(11)
In both expressions we have powers with bases 5 and 10. Recall that powers with the same base have greater values when they have greater exponents. Notice that in the expression 5^2 * 10^(11) both exponents are greater than respective exponents in the expression 5^1 * 10^9.
Number of White Blood Cells
Number of Red Blood Cells
Exponents Comparison
5^1 * 10^9
5^2 * 10^(11)
1<2
5^1 * 10^9
5^2 * 10^(11)
9<11
As we can see, both factors of the number of red blood cells are greater than the respective factors of the number of white blood cells. This means that the number of red blood cells in the donation is greater than the number of white blood cells.
