In everyday life, we use the decimal system using digits 0-9.

Ten digits in total.

The number 25 uses five in the position that is worth one,

and uses two in the position that is worth 10.

It is very likely that the reason behind using 10 digits is that,

it is the number of fingers humans usually have in their hands.

The decimal system is also called base 10.

The worth of each position is called the place value.

The place values in decimal go up by a factor of

10 is always the base number, starting from one.

We read place value from right to left,

with the rightmost place value being one,

then 10, then 100 and so on.

The digits, a word that comes from the Latin word for'

fingers' are multiplied by the place value in order to know the total value.

We use this recipe for any number base.

The key ID number basis is that,

the base number is how many digits are used and the place values starting one

on the right hand side and the next place value

on the left goes up by a factor of the base.

So, base two called binary,

has two digits; zero to one.

The place values are powers of two.

Base 60 called sexagesimal has 60 digits from zero to 59,

and the place values are powers of 60, and so on.

But base numbers aren't a modern thing.

They have been along with us as humans since

the time we started organizing counting for larger numbers.

Number basis allows us to use only a small number of

symbols to write an unlimited quantity of numbers in a systematic fashion.

It is a huge leap from carving notches

on a bone to keep track of how many sheep you keep.

A number sense is not exclusive to humans.

Many mammals and birds have a number sense,

and there is evidence to show such animals being

able to distinguish quantities of one, two,

three some also four and an ability to

compare larger quantities or even fractional quantities such as a half,

a quarter and three quarters.

But we, humans, are a species that took that number sense further and have

mental and physical representations of counting numbers

including the concept of nothing and infinity.

Our species has sculptural needs that require precision.

So, we develop a system for noting down numbers,

making sense of them,

and doing sophisticated operations with them.

We developed routines, algorithms to add up,

subtract, multiply, divide, to keep track of money and goods when trading.

Today, we're still employ mathematicians and computer scientists to work in trading.

Babylonians used the sexagesimal decimal system combined with decimal,

base 10 to make numbers up to 59, the digits.

These digits were then used in place value style with powers of 60.

In sexagesimal, 20, four,

59 means from the right to the left,

59 units four times 60 and 20 times 360 all added up.

So, the expanded form of this number is 20 times 360 plus four times 60 plus 59,

and note, we write from left to right,

from the largest place value to the smallest and this equals to 7,200 plus

240 plus 59 which equals 7,499 in decimal.

Now, are you wondering if the Babylonians had

60 different symbols for the digits zero to 59?

Yes and no.

The genius of it is that they used two symbols only to make all the digits.

They used clay tablets and a stylus.

Really, just a stick,

and pressed the stylus on the fresh clay to make marks like this,

for 10, and like this,

for one, and using base 10,

they organized the marks like in this picture.

This allowed them to make astronomical calculations.

I mean, both as in large numbers and

also as in tracking the movements of the bodies observed in the sky.

The motivation for this system may be that to observe the sky,

it is handy to divide a circle into many small equal parts.

60 is a number with many factors.

It can be divided by one, two, three,

four, five, six, 10,12,15,

20, 30, 60 which is handy when we work out fractions of the denominator 60.

This was a very sophisticated system and Babylonians calculated with fractions,

not just whole numbers.

Looking around cultures across the world,

there is evidence of even other number systems.

The Mayans use the vigesimal system that is base 20.

Although Europe primarily uses decimal systems, in France,

there is evidence of using the Vigesimal as the French word for

80 is four 20s quartre-vingts.

The Chinese number system is decimal but with

the added feature that a symbol for the place value is written after the digits,

as a reminder for the expanded form.

For example, 193 is written as the equivalent of one, hundred, nine,

ten, three with 110 being a symbol for the place value,

one, nine, three being digits.

If that sounds really long,

join me in appreciating a language fit for computation,

the sounds for number words are shorter than the corresponding English words.

In Britain and the US,

the imperial system of measures use basis eight, 12, 14,

16 as there are 12 inches in a foot,

16 ounces in a pound,

14 pounds in a stone,

eight points in a gallon,

all side-by-side with decimal.

Now, the digits we use today in the decimal system come from the Hindu Arabic numerals.

The trading in the Mediterranean gave Europe

access to a much more sophisticated number system,

positional and fit for efficient arithmetic.

In the 12th hundreds,

Leonardo da Pisa also known as Fibonacci,

and himself the son of a trader, popularized these numbers.

Until then in Europe,

the roman numerals were used and these were not suitable

for speedy calculations as the system is not positional.

What I mean is that to add 16,

43, we add the units,

six plus three to give nine,

and the 10s one plus four to give five, and get 59.

With roman numerals, it takes longer as the numbers in each place value are not so clear.

We still measure time using other bases.

What bases are these?