## Estimating Orders of Magnitude

Many calculations in physics involve many powers of ten. It can be hard to gauge whether a calculation is correct or accurate: is the distance to a certain star or There may not seem a lot of difference between the powers in this example, but it corresponds to a factor of 10. It is useful to make a rough estimate before using a calculator. This often be done by adding or subtracting powers when numbers are in standard form.

Example: For more practical purposes it helps to know the masses of many objects in terms of SI units. Some are given below.

1 kg – A packet of sugar or a litre of water. A person might weigh from 50 kg upwards.

1 m – The distance between a persons outstretched hands.

1 s - Duration of a heartbeat.

1 amp – The current consumption of a typical computer.

25 degrees celsius – Roughly room temperature. Actually the SI unit of temperature is Kelvin (K), with 1 degree celsius = 1 degree kelvin.

1 mol – the mass of one mol of a substance is typically from a few grams to a few tens of grams. 1 mol of Carbon 12 is about the number of carbon atoms in a pencil lead.

1 m/s – Walking speed. A car might move at 30 m/s on the motorway.

1 N – About the weight of an apple.

1.5 V – A typical small battery voltage.

10 J – The energy used to lift a bag of sugar to waist height. The typical person uses about 10000 J per day.

500,000 Pa – A typical pressure exerted on the ground by a person standing up. 