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e LEARNING - MATHEMATICS:

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Page 1

TOPIC: NUMBER BASE

WHAT IS NUMBER SYSTEM

Number system is the use of radix or base to represent numbers in numeral system.
Generally, a number X in base n is written as:

The figure(s) of the number 'X' must be less than the number of the base n

For instance if the number 1101 is in base 2; written as:

You will notice that all the figures in the number '1101' are less than the base which is 2.

The number could be 1101 in base 5; written as

It is incorrect to write 1201 in base 2 because the figure '2' in the number 1201 is equal to the base 2.

It is also incorrect to write 1205 in base 3 because the figure '5' in the number 1205 is greater than the base 3.

So note that:

The base of Decimal system is 10.

For instance, number 99 (ninety-nine) in the decimal system is actually:

i.e 99 in base 10

And also number 53 (fifty-three) in the decimal system is:

i.e 53 in base 10

However, the base or radix of the numbers in the decimal system (i.e base 10) are not written. So, when we write number 99 (ninety-nine), we don't have to write the base 10 because we know that number 99 (ninety-nine) is in base 10. The same thing apply to all the numbers in the decimal system.
So,

However, the base of every number that is not in base 10 must be specified in order to distinguish the number. For instance 1101 in base 2 is not the same as 1101 in base 5, and also not the same as 1101. The last number 1101 is in base 10 since the base was not specified.

So,

 

 

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