Q65E - Chemistry (OpenStax)

Question

The diameter of a red blood cell is about 3 × 10^-4 in. What is its diameter in centimeters?

Step-by-Step Solution

Answer

The diameter of a red blood cell is 8x10^-4 cm.

Step 1: Defining the terms inch and centimeters

Inch –

It is a British imperial and US customary system unit for the measurement of length. It is a unit of length or height. It is \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {39.37}}}\right.}\!\lower0.7ex\hbox{${39.37}$}}\) of a meter. It is represented as an inch in units.

 

\(1\,\,{\rm{inch}}\,\, = \,\,2.54\,\,{\rm{centimeters}}\)

Centimeter –

It is a measure of length or height in the CGS unit system. It is one-hundredth of a meter. The capacitance is measured in cm in the CGS unit system. It is one-hundredth of a meter. It is represented by cm in units.

 

\(1\,\,{\rm{centimeters}}\,\, = \,\,0.3937\,\,{\rm{inch}}\)

Step 2: Calculating the diameter of red blood cells in centimeters

We know that 

\(1\,\,{\rm{inch}}\,\, = \,\,2.54\,\,{\rm{centimeters}}\)

Using the conversion factor for inch to centimeters,

 

\[3\, \times \,{10^{ - 4}}\,\,{\rm{inch}}\,\, = \,\,\,\,\,\left( {3 \times \,{{10}^{ - 4}}{\rm{inch}}\, \times \,\frac{{2.54\,\,{\rm{centimeters}}}}{{{\rm{inch}}}}} \right)\,\, = \,\,3 \times \,{10^{ - 4}}\,(2.54)\,\, = \,\,\,7.62\, \times \,{10^{ - 4}}\,{\rm{cm}}\]

Therefore, the diameter of a red blood cell is 7.62x10^-4 cm.

Rounding off to one significant figure, we get the diameter to be 8 x 10^-4 cm.