Review of Scientific Notation

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Presentation transcript:

Review of Scientific Notation 102 = 100, 101=10, 100 = 1, 10-1=0.1, 10-2=0.01 1012=1,000,000,000,000=trillion (Tera-) 109 =1,000,000,000 = billion (Giga-) 106 = 1,000,000 = million (Mega-) 103 = 1,000 = thousand (kilo-) 10-2= 0.01=one-hundredth (centi-) 10-3= 0.001=one-thousandth (milli-) 10-6= 0.000001=one-millionth (micro-) 10-9= 0.000000001=one-billionth (nano-) 5.4x103=5,400 7.05x10-3=0.00705 4,700=4.7x103 0.017 = 1.7x10-2 Start here on 1/9

Powers of Ten Arithmetic Multiplication: (5.3x103) x (6x10-5) = 31.8x103+(-5) =31.8x10-2 = 3.18x10-1 =0.318 = 0.3 One significant figure! Keep only the minimum number of significant figures going into the calculation in the answer. Division: (9.3 x10-4)/(3.10x10-6) = 3.0 x10-4-(-6) = 3.0 x102 = 300 BUT, 3.0x102 is the better answer, as it CLEARLY has two significant figures; scientific notation is PRECISE.

The Scales of the Universe We deal with the largest possible things -- the whole universe -- and with the smallest -- nuclei of atoms. This requires us to use a wide range of PHYSICAL UNITS and we USE THE METRIC SYSTEM. Length: m or cm Mass: kg or g Time: s or yr Temperature: K(elvins) ON 1/18/05 START w/ SLIDE 8 SEASONAL VARIATIONS Radius of Sun = 6.96x10^10cm = 7x10^5 km Mass of Sun = 1.989x10^33g = 2x10^33g = 2x10^30 kg One year = 31.5x10^7 s 1 pc = 3.26 light-yr = 3.085678 x 1018cm=3.1x1013km 1AU = 1.496x1013cm = 150,000,000 km (astronomical unit = mean distance between earth and sun)

Sizes of Everything Universe: open or flat -- infinite; closed -- 1028cm Galaxies: no of stars 109-1013; size ~ 1023cm~3x104pc Stars: 1010-1012cm (most radii) Typical separations: 1018cm ~ 1 pc Planets: RE=6.4x103km = 6.4x108cm Separations: ~ 1 AU Mountain: Tallest ~ 10 km, more typical ~6 km Hm/RE=6.4km/6.4x103km=1.0x10-3 People: 1.5m = 1.5x102cm (~5 feet) Visible light: wavelength=500nm=5x10-5cm Atom: 0.1nm=10-8cm=10-10m (X-ray wavelength) Nucleus: 1 Fermi = 10-13cm = 10-15m Write math symbols for >, >=, equivalent, approx equal, proportional, roughly equal

Time Scales of the Universe Time since the Big Bang: ~1.4x1010 yr Galaxies formed: ~1.3x1010 yr ago Solar system formed: 4.55x109 yr ago Oldest rocks on Earth: 3.8x109 yr BP Earliest life forms: ~3.5x109 yr BP Earliest hominids:~2x106 yr BP Mountains: Appalachians:~2.5x108yr BP; Rockies: 7x107 yr BP Human lifespan: ~75 yr Oscillation time for visible light: ~2x10-15 s Time for light to pass the nucleus of an atom: ~3x10-24s

Astronomy 1020 Lab Requirements Bring to lab next week Astronomy: A Laboratory Textbook, 3rd Ed., by John W. Wilson Metric ruler ~ 30 cm long Protractor Drawing compass Scientific calculator (not a cell phone)