How can absolute value help you to understand the size of a quantity

The absolute value is the size of the quantity regardless the sign and direction. This is, it tells the magnitude.

A quantity may be a scalar or a vector.

Some scalar quantitiies are mass, density, temperature, distance, number of cars. Some scalar quantities only have size (magnitude) but other also have sign, i.e. may be either positive or negative.

Scalar quantities that only have magnitude are like mass, density, or number of cars. For example, 20 grams, 1 g/cm³, and 12 cars, tell all the information about the quantities of mass, density, and cars. In theses examples the absolute value is the quantity: it tells the size of the quantity.

A good example of scalar with sign is temperature. For example, temperature in a hot day may be 30°C, and temperature in a cold day may be - 8°C. You need to include the negative sign to indicate the whole range of temperatures. But the absolute value of the temperature is the magnitude without the sign. The absolute value of 30°C is 30 and the absolute value of - 8°C is 8. Then, the absolute value tells the magnitude or size of the measurement, regardless the sign.

Some examples of vectors are position, velocity and force. To indicate positiion, velocity and force, you need to include the magnitudeand the direction. For example, 30 m at 30° North of the East is a position, 100 km/h East is a velocity, and 2000 newtons 20° above the horizontal line is a force. Yet the absolute value tells you just the magnitude or size of vector quantities. The absolute value tells the magnitude or size of the quantity regardless the direction: 30m, 100km/h, and 2000 newtons are the absolute values of those quantities; they tell you the size of the measurement but not the direction.

Then, the absolute value is always the size of the quantity regardless the sign and direction.

The absolute value is indicated by enclosing the variable inside two bars: | x | is read absolute value of x and is always positive.