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To count, we use the "Base-ten Positional Numeral System” (also called Decimal numeral system).

The word "positional" means that each digit contributes to a specific value in the number directly related to its position in the numeral. It is "decimal" because each unit of numeral is constructed as ten times larger than the previous one.

It is possible to write any number using only 10 digits (0,1,2,3,4,5,6,7,8,9).

This system is often utilized before it is even fully understood, and we do not always realize what each digit of a number represents, especially for very large numbers.

To strengthen this understanding, a proportional representation in cubes makes it possible to build and compare objects whose "size" (here the volume) directly reflects the size of what each digit represents.

This animation allows you to represent all numbers strictly below 100,000,000,000 (100 billion). Some quantities quickly become negligible in front of others. Click on a digit of the number to locate the quantity it represents. It is often difficult to imagine huge quantities. These large numbers take on more meaning if we associate them with a volume so that we can make comparisons:

- Compare the population of Belgium (10 million inhabitants) with that of India (1.3 billion inhabitants).
- Compare the annual drinking water consumption of a Canadian (150,000 liters) to the similar consumption of a Moroccan (25,000 liters).
- Compare the arrival of the first land animals (400 million years ago) and the appearance of homo-sapiens (300,000 years ago).
- Compare the duration of the "Carboniferous" geological period that is at the origin of our hydrocarbon reserves (65 million years) to the probable duration of 300 years for modern man to deplete this resource.

Just click or drag a number to add it to the scene. Click on a symbol on the scene to remove it.

A similar interactive dealing with the scientific notation is available (link).

- To illustrate the construction of numerals from 1 to 100,000,000,000 with the decimal system.
- To switch from writing an integer to its representation and vice versa (decompose and recompose a number digit by digit).
- To visualize the value of a very large number.

The decimal numeral system is now the most used in the world but you should know that other numeral systems have existed: base 5 (5 fingers of the hand), base 12 (duodecimal system so practical…