Background Math Scientific Notation and orders of magnitude IB Physics: Chapter 1 Background Math Scientific Notation and orders of magnitude

Big and Small In Physics, we deal with some very BIG numbers. Blue Marble Atom In Physics, we deal with some very BIG numbers. The mass of the Earth is 5980000000000000000000000 kg. The mass of the Sun is 1989000000000000000000000000000 kg And some very small numbers. The mass of an electron is 0.000000000000000000000000000000911 kg. These numbers are hard to visualize exactly how big they actually are, and even harder to type into your calculator.

Scientific notation. To help we use scientific notation. The rule is: 5980000000000000000000000 kg. becomes 5.9x1024 kg. 0.000000000000000000000000000000911 kg. becomes 9.11x10-31 kg. The rule is: Move the decimal point until only one non-zero digit remains on the left. # of spaces moved is the exponent of 10 If the decimal moved left (ie a big number) the exponent is “+”. If the decimal move to the right (ie a small number), the exponent is “-”.

Practice! 32 000 000 written in scientific notation is? No… try it before you move on! 3.2x107 0.00000436 written in scientific notation is? Come on! Again, try it before you move on! 4.36x10-6 Got it?

Orders of Magnitude We sometimes use the term “Orders of Magnitude”. This is a term that indicates generally how much larger (or smaller) one number is than another. To compare orders of magnitude, we usually just have to look at the exponent of the 10 in scientific notation. Eg. The Earth is 5.98x1024 kg. The Sun is 1.989x1030 kg. We could say that the sun is 6 orders of magnitude more massive than the Earth. 30 (the exponent on the 10 for the sun) – 24 (the exponent on the 10 for the Earth = 6. This means the sun is approximately 1000000 (106) times the mass of the Earth. How many orders of mangitude is the mass of an electron (9.11x10-31 kg) smaller than the mass of a proton (1.67x10-27 kg)

Orders of magnitude How many orders of mangitude is the mass of an electron (9.11x10-31 kg) smaller than the mass of a proton (1.67x10-27 kg) -31—27= 4!!! So an electron is 4 orders of mangitude smaller (ok “less massive”) than an proton. This means that 1 proton is approximately the same as 10000 (or 104!) electrons.

Scientific Notation and your calculator. Your calculator has a button to do scientific notation. If you wanted to do 5.98x1024, DO NOT JUST TYPE THIS IN. Instead use the button that looks like: So you would type 5.98EE24” into your calculator. This means “5.98x1024. (Notice I never put a “10” into that line E EE EXP

Calculators and Scientific notation Practice: Do 5.98x1024 / 9.11x10-31 in your calculator . Did you type 5.98E24÷9.11E-31 If you did, you should get 6.56x1054. But your calculator might actually say 6.56E54

References Atom: Blue Marble: https://pixabay.com/en/atom-electron-neutron-nuclear-power-1222511/ Blue Marble: https://commons.wikimedia.org/wiki/File%3AThe_Earth_seen_from_Apollo_ 17.jpg. By NASA/Apollo 17 crew; taken by either Harrison Schmitt or Ron Evans [Public domain or Public domain], via Wikimedia Commons