# 1.1.3 Estimating Physical Quantities

### Orders of Magnitude

• 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
• 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 the part that indicates the number of zeros after the 1 ie. 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

#### Worked Example

Estimate the order of magnitude for the following quantities:

1. The temperature of the surface of the Sun in Kelvin
2. The power of a standard lightbulb
3. The volume of the room you are in now

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 ~ 103 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

### 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

#### Worked Example

Estimate the energy required for an adult man to walk up a flight of stairs.

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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