V. Scientific Notation
There are two kinds of math, stuff we discover and stuff we make up. Scientific Notation is one of those things we made up. But it works remarkably well. Mathematicians are basically lazy. And Scientific Notation is a short cut.
Keep in mind, I have no way of knowing what you know. Please use the form below to ask questions, I will try to surprise you with a speedy response.
With fractions, you need a common denominator to add or subtract them. We convert things to decimal so our common denominator is always a factor of 10. 1/2 becomes 0.5, 1/4 is 0.25. To add 1/2 and 1/4 you have to find a common denominator. Adding decimals is easy 0.5 + 0.25 is 0.75. It makes life easier. Something similar is happening with scientific notation.
One of many examples is the distance to Alpha Centauri which is about 42,479,700,000, 000 km or 26,395,700,000,000 miles. Converting this to scientific notation we get about 4.25 x 10^10 km or 2.6 x 10^13 miles. Very small numbers use negative powers of 10. 10^-1 is the same as 1/10 or 0.1.
At this point I should clarify a couple of things. I am pretty good at mathematics - Websites - not so much (yet). So, I'm using the ^ symbol to raise a number to a power. 10^10 is ten to the tenth power. I would use a superscript, if I knew how. If you know how - I'd love to hear from you. Another convention that I'm using is the * symbol for times. I would use x but it will get confusing when I have a variable of x in an equation. It's good to get used to both of these conventions as they are used by many programming languages and spreadsheets (the exponent thing, well - I'll change it to a superscript as soon as I learn how).
Not only does it make things easier to write, but, as with fractions, there's a lot you can do with like bases. For instance 10^3 * 10^2 = 10^5. All you have to do is add the exponents 3 + 2 = 5. Why? Well, 10^3 is 10*10*10 and 10^2 is 10*10 so
10^3 * 10^2 = (10*10*10)*(10*10) = 10*10*10*10*10 = 10^5
And it works for division (10^3)/(10^2) = 10^(3-2) = 10^1 = 10. Why? Well (10*10*10)/(10*10) you cancel out the 10's on the top with the 10's on the bottom and you end up with one 10 left in the numerator or = 10.
And - (10^5)^3 = 10^(5*3) = 10^15. Because (10^5)*(10^5)*(10^5) = 10^(5+5+5) = 10^15.
Hopefully, you're getting the idea. Lastly -√(10^6) = 10^(6/2) or 10^3. Because the square route of a number is the same as taking that number to the 1/2 power.
I know - we kind of rushed through this. If you have questions - use the form below to ask. I love questions!.
Where do we use Scientific Notation?
10^-13 Size of a proton - note the negative sign, so this is .0000000000001
10^-12 Weight of a human cell in kg
10^-9 Size of a typical virus in meters
10^-7 Wavelength of visible light
10^-4 Diameter of a human hair
10^4 Depth of the deepest ocean on Earth - in meters
10^10 The distance light travels in a minute, given in meters
Problems
There's some good information from the chemistry department at Texas A&M University. This includes an explanatory chart and information about how to enter information on your calculator.
XIII. Linear Equations
XVII. Real Numbers
XIV. Math Terms
XVIII. Percentages