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Number Systems: Base 10 Decimal

Document Reference: TN200901004 - Rev: 4.32 - Last Update: 22-03-2014 07:28 GMT - Downloaded: 26-Mar-2019 12:57 GMT

The decimal (aka Base 10) number system uses ten symbols for counting and expressing value.

The decimal system as we know it today found its origin in India in the 9th century. Of course, different number systems had been in use by other civilisations before, but they all lacked a symbol for the value of zero. The first recorded use of the symbol '0' as a place value was found on a stone tablet dating back to the year 876. The inscription on this stone tablet concerns a planted garden in the Indian town of Gwalior. It is inscribed that this garden would produce enough flowers for 50 garlands per day, given to a local temple.

The decimal number system arrived in Europe in 1202 with the book titled 'Liber Abaci' by Fibonacci, also known as Leonardo of Pisa. Fibonacci praised the decimal system and explained that any number may be written with the nine Indian figures 1-9 and with the sign 0. Today, the decimal system is the most commonly used system for most calculations and it has no limitation in value representation.

Decimal Symbols and Values

In the decimal number system, the symbols 0 to 9 represent values zero to nine. Unlike other number systems, decimal values generally do not require a specific prefix or suffix. However, in calculations with other number systems you may find decimal values represent by the subscript '10'.

Decimal Symbols Table

Decimal ValueDecimal SymbolPossible Decimal Value Representations
000      or      010
111      or      110
222      or      210
333      or      310
444      or      410
555      or      510
666      or      610
777      or      710
888      or      810
999      or      910

Decimal Digits

The left most digit within a decimal number is the least significant digit (LSD) and has the lowest place value. As further the digits move to the right, as higher the place value becomes. The right most digit within a decimal number is the most significant digit (MSD) and has the highest place value.

Decimal Place Values

6. Digit
From Left
5. Digit
From Left
4. Digit
From Left
3. Digit
From Left
2. Digit
From Left
Left Most
Digit
Power of 10 (10x):105104103102101100
Place Value:100000100001000100101

Decimal Number Line

Example of a number line displaying hexadecimal numbers from -1 to 27 only:

Decimal Number Line

Decimal Counting

Decimal Counting Example

Counting Bananas in Decimal

In above image, let us count all the bananas in decimal. We count as follows:

1 … 2 … 3 … That's it, there are 3 bananas in above image!

Counting Pears in Decimal

Now let us count all the pears in decimal. We count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … 9 … 10 … 11 … That's it, there are 11 pears in above image!

Counting Apples in Decimal

We can also count all the apples in decimal. We count as follows:

1 … 2 … 3 … 4 … 5 … 6 … 7 … 8 … 9 … 10 … 11 … 12 … 13 … 14 … 15 … 16 … That's it, there are 16 apples in above image!

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