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Estimation

Estimation. Rounding. The simplest estimation technique is to round. This works very well on formulas where all the values can be reduced to one significant figure. Order of Magnitude Rounding. Rounding to a power of ten is the crudest form of rounding.

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Estimation

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  1. Estimation

  2. Rounding • The simplest estimation technique is to round. • This works very well on formulas where all the values can be reduced to one significant figure.

  3. Order of Magnitude Rounding • Rounding to a power of ten is the crudest form of rounding. • Order of magnitude estimates are easy to compare since they are all only powers of ten. • For comparison to work, the units need to be the same (meters and meters, not km).

  4. My Height Lecture Hall Faraday West NIU Campus (EW) DeKalb Co (EW) Illinois (EW) USA (north-south) 5’9” = 1.75 m = 2 x 100 m 8 m = 0.8 x 101 m 80 m = 0.8 x 102 m 2000 m = 2 x 103 m = 2 km 28,800 m = 3 x 104 m = 30 km 150 km = 2 x 105 m = 200 km 1900 km = 2 x 106 m = 2 Mm Order of Magnitude These lengths differ by about one order of magnitude. mapquestuses about two steps per order of magnitude.

  5. Geometrical shapes can often be used to approximate real shapes. Geometric formulas Geometric relationships Appropriate shapes can simplify the problem. 2-dimensional (triangle, circle) 3-dimensional (box, sphere). Using Geometry s2 s1 h1 h2

  6. How Big? • Assume the density of a rock is three times that of water. How many centimeters across is a one metric ton (1000 kg) rock? • The rock has a density of 3 g/cm3 • The volume is 106 g / (3 g/cm3) = 3.3 x 105 cm3 • Estimate that the rock is a sphere, V = (4/3) r3 • d = 2r = 2 (3V/4 )1/3 • d = 85.7 cm  90 cm next

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