Converting miles to square meters

[jwainwright09]

Homework Statement

A NASA satellite showed that in 2003 the ozone hole was much larger than it was in 2002. The 2003 hole measured 1.04 X 10(power 7) mi (power 2) in diameter, while the diameter of the 2002 hole was 6.9 X 10(power6) mi (power 2). Calculate the difference in size between the two holes in square meters.

Homework Equations

Calculate the difference in size between the two holes in square meters.

The Attempt at a Solution

I do not even know where to start?!

 

[berkeman]

Homework Statement

A NASA satellite showed that in 2003 the ozone hole was much larger than it was in 2002. The 2003 hole measured 1.04 X 10(power 7) mi (power 2) in diameter, while the diameter of the 2002 hole was 6.9 X 10(power6) mi (power 2). Calculate the difference in size between the two holes in square meters.

Homework Equations

Calculate the difference in size between the two holes in square meters.

The Attempt at a Solution

I do not even know where to start?!

Welcome to the PF.

The first thing would be to put your numbers into a little more readable format using LaTeX:

$2003: 1.04 * 10^7 mi^2$

$2002: 6.9 * 10^6 mi^2$

Then you can do the subtraction to find what the difference is in mi^2.

To do units conversions, the trick is to multiply by 1, where the "1" is a special 1 that has the correct units on the top and bottom of a fraction, to help you cancel out the units you want to get rid of, and be left with the units you want.

So for example, to convert from kilometers to meters, you would do this:

$$5km * \frac{1000m}{1km} = 5000 m$$

See how the meters cancels out in the numerator and denominator, leaving you with the correct units?

Now just be careful when dealing with squared units, like this:

$$5km^2 * (\frac{1000m}{1km})^2 = ? m^2$$

Now are you able to do you problem?

 

[berkeman]

BTW, I just noticed an error in your post. You give the areas of the holes in mi^2, but then call those numbers diameters. That can't be right...

 

[jwainwright09]

Yes, this helps so much. Thank you for making this clearer to me. I worked the problem and the answer I come up with is 0.35 x 10^7 mi^2. Thanks again!

 

[asteriatic]

I would first convert the measurements from miles to square meters. This can be done by using the conversion factor of 1 mile = 1609.34 meters.

2003 hole: 1.04 x 10^7 mi^2 = (1.04 x 10^7 mi^2) x (1609.34 m/mi)^2 = 1.04 x 10^7 mi^2 x 2.59 x 10^6 m^2/mi^2 = 2.69 x 10^13 m^2

2002 hole: 6.9 x 10^6 mi^2 = (6.9 x 10^6 mi^2) x (1609.34 m/mi)^2 = 6.9 x 10^6 mi^2 x 2.59 x 10^6 m^2/mi^2 = 1.79 x 10^13 m^2

Now, to find the difference in size between the two holes, we can simply subtract the two values:

2.69 x 10^13 m^2 - 1.79 x 10^13 m^2 = 0.9 x 10^13 m^2

Therefore, the difference in size between the two holes is approximately 0.9 x 10^13 square meters. This shows that the 2003 hole was about 0.9 x 10^13 square meters larger than the 2002 hole. This information can help us understand the changes in the ozone layer over time and the potential impact on our environment.