Question

Rhinoviruses, which are the leading cause of the common cold, have a diameter of 20 nanometers (20 × 10−9 meter). Pneumococcus, a bacterium causing pneumonia, measures about 1 micron (10−6 meter) in diameter. How many times as large in diameter as the virus is the bacterium?

Answer 1

Answer:

The bacterium Pneumococcus is 50 times as large in diameter as the Rhinovirus.

Step-by-step explanation:

As we can see, the bacterium is larger than the virus:

The diameter of the bacterium is:

$\\ Bacterium_{diam} = 1*10^{-6}m = \frac{1}{10^{6}}m = \frac{1}{1000000}m$

The diameter of the virus is:

$Virus_{diam} = 20*10^{-9}m = \frac{20}{10^{9}} = \frac{20}{1000000000}m$

Since the denominator is much greater in the case of virus' diameter compared with the bacterium's diameter, the virus' diameter is smaller than the bacterium' diameter, but how much bigger is the bacterium's diameter?

This is a simple ratio:

$\\ \frac{Bacterium_{diam}}{Virus_{diam}}$

The former tells us how many times the Bacterium's diameter is larger than the virus' diameter.

Then

$\\ \frac{Bacterium_{diam}}{Virus_{diam}} = \frac{1*10^{-6}m}{20*10^{-9}m}$

$\\ Since\; \frac{10^{9}}{10^{9}} = 1, then:$

$\\ \frac{1*10^{-6}}{20*10^{-9}} = \frac{1*10^{-6}}{20*10^{-9}}*\frac{10^{9}}{10^{9}}$  

$\\ \frac{1*10^{-6}*10^{9}}{20*10^{-9}*10^{9}}$

$\\ \frac{1*10^{-6+9}}{20*10^{-9+9}}$

$\\ \frac{1*10^{3}}{20*10^{0}}$

$\\ \frac{1*10^{3}}{20*1}$

$\\ \frac{1000}{20} = \frac{100}{2} = 50$

Therefore, the bacterium is 50 times as large in diameter as the virus.