## Numbers

Scientists have a system for reading and reporting measurements that uses standard units of measurement and shorthand notation for large numbers. Since you will be taking data, you will want to be able to communicate exactly what your data is measuring in a way that everyone can understand.

- Units
- Scales
- Fractions

Being familiar with the different ways of reporting numbers and measurements is crucial for communicating science. This applies to all scientific endeavors, whether you're reading your detector, studying results, reporting results, or reading manuals.

** Units:** A unit is an amount that defines measurements. For example, the units of length or distance could include inches, feet, meters, miles, etc. But you woulnd't use these units for weight; you would use grams or pounds. In many situations, for numbers to be meaningful, they must include units. We could measure the distance we drive in our cars in inches, but that just isn't convenient. Miles is a much better unit for distances traveled by cars.

** Standards:** What if we told everyone to use the size of their foot to measure a "foot"? Since everyone has different sized feet, they would all measure different lengths. To keep consistency from measurement to measurement, we have adopted standards, so everyone using these standards makes the same measurements.

The two most common standards are United States Customary Units and the International System of Units (SI) Metric System. You are probably more familiar with US units like feet, miles, and degrees Fahrenheit, but most other countries use Metric Units such as meters, grams, degrees Celsius. The table at right shows typical measurements in the different systems and gives equivalent values, so you can convert back and forth. One thing you should note is the SI units for temperature could be Cesius OR Kelvin. Kelvin is used most commonly in sceintific measurements of temperature, because it has no negative values. You can read more about Kelvin and how to convert with Celsius and Fahrenheit on Wikipedia.

Numbers can drastically range in size. The scale of an object gives an idea of how large or small it is.

** Scientific Notation:** Scientific Notation is a quick, shorthand way to write very large or very small numbers, especially useful for SI units since they have base 10. Wikipedia does a great job explaining how to write numbers in scientific notation, so look it over.

image from www.kylesconverter.com

We can simplify things further by naming certain extensions in scientific notation. To give an example, we don't just use meters to measure distance, because it would get cumbersome to say that we went 78,000 meters or even 78 x 10^{3} meters. We use the prefix "kilo" as shorthand to mean 1000 or 10^{3} times the base unit of meters, so we just say 78 kilometers, much easier. The table at the right lists some prefixes. You can see "centi" for 10^{-2} or 100 times less than the base unit, which, of course, describes how there are 100 centimeters in a meter.

** Orders of Magnitude:** An order of magnitude is the number of times a number is multiplied by 10; it is the exponent in scientific notation. So a kilometer is 3 orders of magnitude greater than a meter, because we have to multiply a meter by ten 3 times to make a kilometer. A megameter is 6 orders of magnitude greater than a meter, but only 3 orders of magnitude greater than a kilometer.

Now that you know about the huge differences between each order of magnitude, you may appreciate this power of ten zoom of our universe, going from the very large and zooming in by a factor of 10 in each segment to the very small.

Fractions represent parts of a whole. For example, this pizza has been cut in 8 pieces, meaning that 1 piece is 1/8 of the whole pizza.

Fractions are ratios. They compare the numerator to the denominator with division. If you perform the division you get a decimal. For example, 1/8 is 1 divided by 8, giving 0.125. And 3/5 is 3 divided by 5, which is 0.30.

And decimals are easily read as percentages. So 1/8 equals 0.125 implies that 1 is 12.5% of 8. Eating one piece of pizza is eating 12.5% of the pizza. Two pieces are 25%, and so on.

Understanding how fractions, decimals, and percentages are all related will help you most with the remote sensing project. Calculating NDVI values requires decimals, and you need to understand what it means to say that RED light having a value of 0.25 means that 25% of all the light received by the detector is in the red range.