Question

Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of 1.50μm2. Convert this to square meters.
Express your answer in square meters.

Answer 1

Create your conversion factors.

You know that 1 micrometer = 1/1000000 m

Then,

[1 micrometer]^2 =[1/1000000 m]^2 =>

=> 1 = [1000000]^2 micrometer^2 / m^2

Now multiply the given area times your conversion factor:

1.50 (micrometer)^2 * [1/1000000]^2  micrometer^2 / m^2 = 1.50*10^(-12) m^2

Answer: 1.50*10^(-12) m^2

Answer 2

The area covered by a certain bacterium is equivalent to 1.5 x 10^-12 square meters.

FURTHER EXPLANATION

This is an example of conversion within the metric system.

To begin, it is important to remember some basic conversion:

• 1 meter (m) = 1,000,000 micrometers (μm)
• 1 meter (m) = 1000 millimeters (mm)
• 1 meter (m) = 100 centimeters (cm)
• 1 kilometer (km)= 1000 meter (m)

The relationships above may be used to convert from one unit to another.

In solving the problem it is first important to get the conversion from μm2 to m2 since it is not directly given among the basic conversions.

First, start with what is known:

$1 \ m \ = 1,000,000 \mu m$

Square both sides:

$(1 \ m)^2 \ = (1,000,000 \ \mu m)^2\\1 \ m^2 = 10^{12} \ \mu m$

Now that the conversion from μm2 to m2 is known, proceed with the given and convert as show below:

$area \ = (1.50 \ \mu m^2 )(\frac{1 \ m^2}{10^{12} \ \mu m^2})\\\boxed {area \ = 1.50 \ x \ 10^{-12} \ m^2}$

Since a meter is much larger than the micrometer, a small value in micrometers will be equivalent to an even smaller numerical value in meters. The value 1.50 x 10^-12 m2 makes sense as this is a very very small number.

LEARN MORE

• Metric System brainly.com/question/3623718
• Dimensional Analysis brainly.com/question/1557970

Keywords: metric conversion