Math and Measurement
Quantities vs. Numbers
Calculations in science are most often done with quantities and not simply with numbers. Anything that can be measured in the physical world is described by specifying a quantity.
A quantity has a magnitude which describes the size of its value, but perhaps more importantly it has a unit which describes what the quantity measures.
A quantity has a magnitude which describes the size of its value, but perhaps more importantly it has a unit which describes what the quantity measures.
Consider the following statement: My cake recipe calls for 3 flour. What does the "3" represent? Does the cake need 3 c (cups), or 3 kg (kilograms), or 3 lb (pounds). The unit must be included to make the quantity meaningful.
A scientist often collaborates with other scientists from around the world. Even if their spoken language is not the same, the language used to communicate the ideas of science must the same for everyone. Measurements in science are made using the Systeme International d'Units, which translates to International System of Units which is usually just referred to as SI units.
Since physics deals with everything in the universe you might expect a vast number of different SI units would be needed. Actually there are only SEVEN base units defined in SI. A base unit is used to measure some fundamental quantity of the physical world.
| Quantity | SI Name | Unit |
|---|---|---|
| mass | kilogram | kg |
| length | meter | m |
| time | second | s |
| electric current | Ampere | A |
| temperature | Kelvin | K |
| amount | mole | mol |
| luminous Intensity | candela | cd |
Notice that the SI base unit for mass is NOT a gram but a kilogram (1 kilogram = 1000 grams).
A gram is a very small amount of mass, 1 gram of water would be the size of a small cube that is 1 centimeter to a side ( 1 cm x 1cm x 1cm = 1 cm3 or 1 mL, about the size of the fingernail tip of the pinky finger).
It was easier to maintain a standard mass equal to 1 kilogram. Physics is said to work in MKS units, which stands for meters, kilograms, and seconds.
It was easier to maintain a standard mass equal to 1 kilogram. Physics is said to work in MKS units, which stands for meters, kilograms, and seconds.
There are many more quantities to measure other than the seven basic ones listed in the table above. Every other physical quantity measured in physics is measured in a derived unit. A derived unit is a combination of other units. Sometimes a derived unit is given a its own name, other times the combination of units is simply written out.
Here is a listing of some common derived units.
Here is a listing of some common derived units.
| Quantity | SI Name | Derived Unit | Combined Unit |
| area | | | m2 |
| speed | | | m/s |
| acceleration | | | m/s2 |
| force | newton | N | kg•m/s2 |
| energy | joule | J | kg•m2/s2 |
| power | watt | W | J/s |
| pressure | pascal | Pa | N/m2 |
| Celsius temperature | Celsius | ºC | [K] + 273.15 |