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.  Order of magnitude estimates are easy to compare since they are all only powers of ten.  For a comparison to work, the units need to be the same (meters and meters, not km).

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/cm 3 so the volume is 10 6 g / (3 g/cm 3 ) = 3.3 x 10 5 cm 3.The rock has a density of 3 g/cm 3 so the volume is 10 6 g / (3 g/cm 3 ) = 3.3 x 10 5 cm 3. Estimate that the rock is a sphere, V = (4/3)  r 3Estimate that the rock is a sphere, V = (4/3)  r 3 d = 2r = 2 (3V/4  ) 1/3d = 2r = 2 (3V/4  ) 1/3 d = 85.7 cm  90 cmd = 85.7 cm  90 cm

Using Geometry  Geometrical shapes can often be used to approximate real shapes.  The standard formulas from geometry can be used to make an estimate.  Shapes can be 2-dimensional (triangle, circle)  Or 3-dimensional (box, sphere).

Triangles  Equal ratios  Right triangles h2h2 h1h1 s1s1 s2s2 s t r 

Apparent Shift  A moving observer sees fixed objects move.  Near objects appear to move more than far objects.  Telephone poles whip by faster than distant trees.  The effect is due to the change in observation point, and is used by our eyes for depth perception. base angle A angle B

Observing Parallax  Observe an object against the background.  Shift one seat left and observe again.  Subtract to get the parallax shift next