Estimation and Orders of Magnitude

The order of magnitude of a quantity is its size given to the nearest power of ten. For example, 2 × 10⁵ J has an order of magnitude of 10⁵ J. Orders of magnitude let you compare very different sizes quickly: an atom is about 10⁻¹⁰ m across and a nucleus about 10⁻¹⁵ m, so an atom is about 10⁵ times wider than its nucleus.An estimate is an approximate value found using sensible, rounded values for the quantities involved. Estimates are usually worked to one significant figure. They let you check whether a calculated answer is sensible and answer questions where exact data are not available.Useful values to remember: mass of an adult about 70 kg, height about 2 m, mass of a car about 1000 kg, speed on a motorway about 30 m s⁻¹, g about 10 m s⁻².Worked example 1: Estimate the kinetic energy of a car in town.
m ≈ 1000 kg, v ≈ 20 m s⁻¹E_k = ½mv² = ½ × 1000 × 20² = 2 × 10⁵ JSo the order of magnitude is 10⁵ J.Worked example 2: Estimate the number of seconds in a year: 365 × 24 × 3600 = 31 536 000 s, which is about 3 × 10⁷ s.State the assumptions you make (for example, the value you chose for the mass), so that someone else can follow the estimate.