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Some math for astronomy

Some math for astronomy. Astronomy 115, Spring 2013. Scientific Notation:. Scientific notation is a shorthand way of writing and multiplying large (and small) numbers. 1,000,000,000,000. 10 12. terra (T) (trillions). 1,000,000,000. 10 9. giga (G) (billions). mega (M) (millions).

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Some math for astronomy

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  1. Some math for astronomy Astronomy 115, Spring 2013

  2. Scientific Notation: Scientific notation is a shorthand way of writing and multiplying large (and small) numbers. 1,000,000,000,000 1012 terra (T) (trillions) 1,000,000,000 109 giga (G) (billions) mega (M) (millions) 1,000,000 106 kilo (k) (thousands) 1000 103 unity 1 100 centi (c) (hundredth) 0.01 10-2 milli (m) (thousandth) 0.001 10-3 0.000001 10-6 micro () (millionth) 0.000000001 10-9 nano (n) (billionth)

  3. Using Scientific Notation: To do numbers that are not divisible by ten, we multiply by an exponential number. 4,275,000,000 = 4.275 x 1,000,000,000 = 4.275 x 109 0.000374 = 3.74 x 0.0001 = 3.74 x 10-4

  4. Using Scientific Notation: To multiply numbers using scientific notation, we add the exponents. 103 x 10-9 = 10(3) + (- 9) = 10-6 102 x 105 = 10(2) + (5) = 107 To divide numbers using scientific notation, we subtract the exponents. = 10(3) - (- 9) = 1012 = 10(2) - (5) = 10-3

  5. Using Scientific Notation: To raise a number to a power, we multiply the exponents To changing from division to multiplication, we change the sign of the exponent

  6. Using Scientific Notation: To add or subtract numbers using scientific notation, we work in front of the exponents, but they must have the same exponent. 3.0 x102 + 2.6 x 105 = 0.003 x 105 + 2.6 x 105 = 2.603 x105 1.0 x105 - 7.0 x 102= 1.0 x105 - 0.007 x105 = 0.993 x105

  7. Scientific Notation /Units Example 1 How long does light take to travel from the visible surface of the Sun to the Earth? Distance from Sun to Earth D = 150,000,000 km This is also known as one astronomical unit (AU) In scientific notation D = 1.5  108 km

  8. Scientific Notation /Units Example 1 How long does light take to travel from the visible surface of the Sun to the Earth? There are 1000 m = 103 m = 1 km: Hence, in meters:

  9. Scientific Notation/Units Example 1 How long does light take to travel from the visible surface of the Sun to the Earth? The speed of light c = 3 x 108 m/s OR

  10. Scientific Notation/Units Example 1 How long does light take to travel from the visible surface of the Sun to the Earth?

  11. Scientific Notation/Units Example 2 Density of Water Density is mass per volume For water: 1 gram / centimeter3 (1g/cm3) What is this in kilograms / meters3 ?

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