Question

madame du sang tests her husbands blood and finds he has a hematocrit of 45%, which means he likely has 2.25 liters of red blood cells throughout his body. the volume of a single red blood cell is approximately 9 × 10^{-14} liters. how many red blood cells are in monsieur du sangs body? a 2.5·10^{13} cells b 2.5·10^{14} cells c 5.0·10^{13} cells d 5.0·10^{14} cells

Explanation:

Step1: Set up the formula

The number of red - blood cells \(n=\frac{\text{Total volume of red - blood cells}}{\text{Volume of a single red - blood cell}}\). Let \(V = 2.25\) liters (total volume of red - blood cells) and \(v=9\times10^{-14}\) liters (volume of a single red - blood cell). Then \(n=\frac{V}{v}\).

Step2: Substitute the values

Substitute \(V = 2.25\) and \(v = 9\times10^{-14}\) into the formula: \(n=\frac{2.25}{9\times10^{-14}}\).

Step3: Simplify the fraction

First, simplify \(\frac{2.25}{9}=0.25=\frac{1}{4}\). Then, using the rule of dividing exponents \(\frac{a}{b\times10^{c}}=\frac{a}{b}\times10^{-c}\) (in the form of \(\frac{2.25}{9\times10^{-14}}=\frac{2.25}{9}\times10^{14}\)), we get \(n = 0.25\times10^{14}\).

Step4: Rewrite in scientific notation

Since \(0.25\times10^{14}=2.5\times10^{13}\) (because \(0.25=\frac{1}{4}\) and \(0.25\times10^{14}=\frac{1}{4}\times10^{14}=2.5\times10^{13}\)).

Answer:

A. \(2.5\cdot10^{13}\) cells