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What do we call quantities that are not derived from other quantities?


Kim sends Philip a recipe for baking a cake. The recipe says to add in some flour, a few eggs, a little bit of milk, a handful of sugar and a hint of baking powder. Then to bake it in a very hot oven for an average length of time. How much is some flour? What about an average amount of time?

Is that 15 minutes or one hour? Philip ends up with a messy mixture. And he doesn't know what temperature to set the oven to. All of these words describe amounts that are different for different people. Philip's hand might be smaller than Kim's.

A few eggs might mean seven to Philip and three to Kim. Instead of saying a little bit of milk, you could say one quarter of a liter. Anyone with a measuring cup could measure one quarter of a liter. Measurements allow people to communicate the quantities of things to one another so that both people know exactly what amount the other person is referring to. Measurement comes from the Greek word metron, which means limited portion.

A meter ruler consists of a set of small, identical spaces that are lined up to make up one meter. If two people use a meter ruler they are both working with the same quantities of measurement. The quantities are standard. A balance gives the quantity of mass in kilograms. A stopwatch measures time in seconds.

Meters, kilograms and seconds are standard measurements. They are the same everywhere in the world. A ruler, a balance and a stopwatch are standard measuring tools. Quantities like a handful, a lot, a little bit, a heartbeat and a footstep are different depending on who is using them. They are non-standard measurements.

In all sciences only standard units are acceptable for measuring. This allows everyone to work within the same system. If you do an experiment with a car and say that it weighed one thousand kilograms and drove twenty thousand meters in thirty thousand seconds, any person who knows standard measurements would know how heavy the car was, how far it travelled and how long it took to travel that distance. So what if you wanted to know the speed of the car? You would divide the distance by the time.

The car's speed is zero-point-six-seven meters per second (0.67m/s). Speed is made up of length and time. It is derived from those two quantities. Length and time are not derived from anything. They are fundamental quantities.

The same goes for mass. It's measured in kilograms. There are other quantities that are made up of fundamental quantities. The area of an object is found by multiplying two lengths. It's measured in square meters.

It's derived from two length measurements. Volume is made up of three different length measurements. And force is made up of mass, in kilograms, and acceleration, which in turn is made up of meters and seconds. Speed, area, volume, and force are considered derived quantities since they are made up of fundamental quantities, like mass, length and time. After learning standard measurements Philip gets a different recipe from Kim.

Now that's something he can work with.