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
Estimating Physical Quantities Table