Kilo Mega Giga

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 build this intuition, 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.

Scientific notation is a way to simplify the writing of very large numbers (and also very small ones). This involves approximating the number with a narrow number of digits: The significant digits.

Note: Numbers are to scale in the illustrations.

• To imagine the large numbers up to 100 billion.
• To estimate large numbers and find an approximate value.
• To understand the notion of significant figures.
• To understand the meanings of KILO, MEGA, GIGA prefixes.
• To write large numbers using scientific notation.

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 when manipulating fractions and multiples), base 20 (which persists in some language like in French where "eighty" is written “quatre-vingt”), base 60 (so convenient for time measurement and trigonometry).

To mark all possible positions of a number, however, it is necessary to define the 0, as a digit but also as a number that is worth nothing.

The first preserved written record of the 0 would be found in the Bakshali manuscript (3rd or 4th century AD) in India.

These 10 digits arrived in Europe under the name of Arabic numerals, because it was actually the Arabs who spread them in the 8th century in their empire that stretched from the borders of India to the Maghreb, then to Spain.

In the 12th century, European mathematicians like Fibonacci understood the interest of this numeration compared to the Roman numeral especially to conduct and write calculations.

It should be said that it was not until the 15th century that decimal system notation was generalized in the scholarly world.