Estimating Physical Quantities (AQA A Level Physics)

Orders of Magnitude

• 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

Estimating Physical Quantities

• 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