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

2. 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 kg.
The mass of the Sun is kg
And some very small numbers.
The mass of an electron is kg.
These numbers are hard to visualize exactly how big they actually are, and even harder to type into your calculator.

3. Scientific notation. To help we use scientific notation. The rule is:
kg. becomes 5.9x1024 kg.
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 “-”.

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

5. 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 (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)

6. 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 (or 104!) electrons.

7. 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 “5.98x (Notice I never put a “10” into that line E EE
EXP

8. 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

9. References Atom: Blue Marble:
Blue Marble:
17.jpg. By NASA/Apollo 17 crew; taken by either Harrison Schmitt or Ron Evans [Public domain or Public domain], via Wikimedia Commons