Scientific Notation & Estimates

What you see depends on where you are! Your local sky – your view depends on your location on earth

Look North in Westerville

Look North on Hawai’i

Resume: Activity: Position Get out your activities book Form a group of 3-4 people Work on the questions Hand in a sheet of paper with the title of the activity and the names of the group members I’ll come around to help out !

Local Sky Depending on your location on earth you see completely different stars! Some stars are always visible, they are circumpolar.

Local Sky (cont’d) The local sky at 40 degrees latitude

Scientific Notation, Estimates, Measurements & Units Scientific Notation increases readability, simplifies calculations Many times a (very) rough estimate is all that is needed to debunk a claim Sometimes even a check of units will disqualify an argument

Scientific Notation 10 8 means multiply 1 by 10 eight times –10 8 is 1 followed by 8 zeroes –Example: 1.5  10 8 km = 150,000,000 km (dist. to sun) A negative exponent means divide instead of multiply: –10 –9 means divide 1 by 10 nine times –Example: 5  10 –9 m = m (yellow light) To multiply, add exponents –Example: 10 4  = = To divide, subtract exponents –Example: 10 4 / = 10 4 – 23 = 10 –19 –Note: 1 / 10 4 = 10 0 / 10 4 = 10 –4

Significant Figures There is an uncertainty with every measurement  reflect this in the number of digits used in quoted results Do not count trailing or leading zeros Examples: –12.3 (3 sig figs) –1.23 (3), 0.45 (2), (3), 1200 (2) – (3)

Estimates Scientists often use a “back of the envelope” calculation to get a sense for how big a number should be Recipe: round every number involved up to one sig fig and keep the exponent

Think inside the box! In essence, mathematics is a set of line by line instructions Use them diligently, and a lot of problems become mere exercises, i.e. tedious but straightforward

Fermi Questions Attributed to Enrico Fermi Try to get the order of magnitude of a quantity with very little data available Making a crude estimate is better than not doing anything

Example: Parcel of the Earth The land area of the earth is divided up into equal parcels for each person on earth. How much would you get? –Need area of earth –Area of land –# People on earth