Question

1. there are approximately ( 5\times10^{6} ) red blood cells per microliter in human blood.

a. if 1 liter is ( 1\times10^{6} ) microliters, how many red blood cells would be contained in 1 liter? express the answer in scientific notation.
b. an average adult male (weighing 160 pounds) has a blood volume of approximately 5 liters. how many red blood cells would he be expected to have? express the answer in scientific notation.

Explanation:

Step1: Calculate red - blood cells in 1 liter

Multiply the number of red - blood cells per microliter by the number of microliters in 1 liter.
$$(5\times10^{6})\times(1\times10^{6})$$
Using the rule \(a^{m}\times a^{n}=a^{m + n}\) and \((a\times10^{m})\times(b\times10^{n})=(a\times b)\times10^{m + n}\), we have \(5\times1\times10^{6+6}=5\times10^{12}\)

Step2: Calculate red - blood cells in 5 liters

Multiply the number of red - blood cells in 1 liter by 5.
$$(5\times10^{12})\times5$$
Using the rule \((a\times10^{m})\times b=(a\times b)\times10^{m}\), we get \(25\times10^{12}\). But in scientific notation \(a\times10^{n}\) where \(1\leqslant a<10\), so \(25\times10^{12}=2.5\times10^{13}\)

Answer:

a. \(5\times 10^{12}\) red - blood cells
b. \(2.5\times 10^{13}\) red - blood cells