1.1.3 Estimating Physical Quantities

• When a number is expressed in an order of 10, this is an order of magnitude.
  • Example: If a number is described as 3 × 10⁸ then that number is actually 3 × 100 000 000
  • The order of magnitude of 3 × 10⁸ is just 10⁸

• Orders of magnitude follows rules for rounding
  • The order of magnitude of 6 × 10⁸ is 10⁹ as the magnitude is rounded up

• A quantity is an order of magnitude larger than another quantity if it is about ten times larger
• Similarly, two orders of magnitude would be 100 times larger, or 10²
  • In physics, orders of magnitude can be very large or very small

• When estimating values, it’s best to give the estimate of an order of magnitude to the nearest power of 10
  • For example, the diameter of the Milky Way is approximately 1 000 000 000 000 000 000 000 m

• It is inconvenient to write this many zeros, so it’s best to use scientific notation as follows:

1 000 000 000 000 000 000 000 = 1 × 10²¹ m

• The order of magnitude is 10²¹
• Orders of magnitude make it easier to compare the relative sizes of objects
  • For example, a quantity with an order of magnitude of 10⁶ is 10 000 times larger than a quantity with a magnitude of 10²

Order of Magnitudes Table

1. The temperature of the surface of the Sun in Kelvin

• • The temperature of the surface of the Sun is about 6000 K
  • This is an order of magnitude of ~ 10⁴ K

2. The power of a standard lightbulb

• • The power of a standard lightbulb is about 60 W
  • This is an order of magnitude of ~ 10² W

3. The volume of the room you are in now

• • This depends on the room you are in
  • The shape should roughly be cubic or (rectangular) cuboid
  • Volume = length × width × height
  • For a cubic room with length 3 m, volume = 3³ = 27 m³
  • This is an order of magnitude of ~ 10 m³

• There are important physical quantities to learn in physics
• It is useful to know these physical quantities, they are particularly useful when making estimates
• A few examples of useful quantities to memorise are given in the table below (this is by no means an exhaustive list)

Estimating Physical Quantities Table