We often talk about quantities and measurements. When we say Millie weighs 6 kilograms, her tail is 25 centimeters long, and today it’s 23 degrees, we are using numbers and units of measurement: kg, cm, and degrees Celsius. Each unit of measurement refers to a measurement scale. Here are some examples:

• In New Zealand and in Europe, we use a thermometer with the Celsius scale, while Americans use a thermometer with the Fahrenheit scale. Our 23 degrees Celsius are 73.4 degrees Fahrenheit.

• On our rulers, we have the metric scale, based on meters, centimeters, etc., while they use inches and feet. Millie’s tail is almost 10 inches long, which is equal to 25 cm.

• On scales, we use kilograms, and they use pounds. Millie’s 6 kg are 13.2 pounds.

The essential thing in these types of measurements is that, once we choose a scale, the result is a number and a unit of measurement: 6 kg, 2 hours, 3 km, 30 degrees. Mass, time, length, and temperature are examples of scalar quantities because their measurement is completely defined by a number and a scale.

Not all quantities are scalar, because sometimes a number and a unit of measurement are not enough to give us all the information. For example, if Millie says, "Yesterday, I walked 10 km," we wouldn’t know where she went because you can walk 10 km in many directions.

To measure speed and force, it is also important to know the direction. These types of quantities are called vector quantities, and their measurement is indicated by a number, a unit of measurement, and a vector, an arrow that shows the direction.

Let’s look at an example to better understand the difference between scalar and vector quantities: the distance traveled is a scalar quantity, while displacement is a vector. Displacement is a straight line between the starting point and the endpoint, which is the shortest distance between those two points. In this figure, we can see that the vector representing the displacement is always the same, but the distance traveled can vary a lot.

The length of the vector depends on the corresponding scalar quantity.